design notes and statistical tables

8/2/2019 Design Notes and Statistical Tables

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Design Notes&

Statistical Tables


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CONTENTS

1. Highway Capacity Design (Older Version).....012. Highway Design ..033. Highway Capacity Design (HCM2000)..114. Traffic Incident Analysis 315. Traffic Signal Design Summary .336. Geometric Design Equations...377. Marshall Mix Design Criteria..388. Roadway Design..399. Key to Structural Catalogue ....4310.Statistical Tables .53


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1. Highway Capacity Design (HCM 1986)Determination of Level of Service

Vv =

PHF

where, v = flow rate for 15 minutes total flow for both directions in vphV = full hour volume total for both directions in vph

PHF = Peak Hour Factor

Service flow rate for two-lane roads on general terrain segments is given by the equation

SFi = 2800 x (v/c)i x fd x fw x fHV

where, SFi is the total service flow rate in both directions for prevailing

roadway and traffic conditions for level of service i in vph

(v/c)i is the ratio of flow rate to ideal capacity for level of service i

fd is the adjustment factor for directional distribution of traffic

fw is the adjustment factor for narrow lanes and restricted shoulder widths

fHV is the adjustment factor for the presence of heavy vehicles in the

traffic stream where,

fHV = 1/ [1+ PT (ET 1) + PB (EB 1) ]

and, PT = Proportion of trucks in the traffic stream

expressed as a decimal

PB = Proportion of buses in the traffic stream

expressed as a decimal

ET = Passenger Car Equivalent for trucks

EB = Passenger Car Equivalent for buses


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Service flow rate for two lane roads on specific grade segments for any upgrade speed is

given by the equation:

SFi = 2800 x (v/c)i x fd x fw x fg x fHV

and, fg = 1/ [ 1+ ( Pp Ip ) ]

fHV = 1/ [ 1+ PHV ( EHV 1 )

Ip = 0.02 ( E E0 )

EHV = 1+ ( 0.25 + PT/HV)( E 1)

where, SFi = Service flow rate for LOS i or speed i, total vph in both directions for

prevailing roadway and traffic conditions

(v/c)i = volume/capacity ratio for LOS i or speed i

fd = adjustment factor for directional distribution of traffic

fw = adjustment factor for narrow lanes and restricted shoulder widths

fg = adjustment factor for the effects of grades on passenger cars

fHV = adjustment factor for presence of heavy vehicles in the upgradetraffic stream

Pp = proportion of passenger cars in the upgrade traffic stream, expressedas a decimal

Ip = impedance factor for passenger cars

PHV = total proportion of heavy vehicles in the upgrade traffic stream

EHV = passenger car equivalent for specific mix on heavy vehicles presentin the upgrade traffic stream

E = base passenger car equivalent for a given percent of grade and agiven speed

E0 = base passenger car equivalent for zero percent grade and a given

upgrade speed

PT/HV = proportion of trucks among heavy vehicles


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2. Highway DesignTable 2.1 Equivalent Passenger Car Unit (PCU) Factors

For two-lane, two-way roads

Vehicle Type PCU FactorFlat Terrain Rolling Terrain Mountainous Terrain

PassengerCar 1.0 1.0 1.0

Small Bus 2.0 3.4 6.0

Large Bus 2.2 5.0 10.0

Light Truck 2.0 4.0 7.0

Medium Truck 2.2 5.0 10.0

Heavy Truck 2.2 5.0 10.0

Motor Cycle 0.5 0.5 0.5

Bicycle 1.0 1.0 1.0

Animal Drawn Carts 4.0 10 24.0

Source: Road Development Authority, Traffic and Planning Division

Table 2.2 Equivalent Passenger Car Unit (PCU) Factors

For multilane roads

Vehicle Type PCU Factor

Flat Terrain Rolling Terrain Mountainous Terrain

PassengerCar 1.0 1.0 1.0

Small Bus 1.5 3.0 5.0Large Bus 1.7 4.0 8.0

Light Truck 1.7 4.0 8.0

Medium Truck 1.7 4.0 8.0

Heavy Truck 1.7 4.0 8.0

Motor Cycle 0.5 0.5 0.5

Bicycle 1.0 1.0 1.0

Animal Drawn Carts 4.0 10.0 24.0

Source: Road Development Authority, Traffic and Planning Division


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Table 2.3 Level of Service criteria for general two-lane highway segmen

v/c ratio ( ratio of flow rate to an ideal capacity of 2800 pcph in both direct

LOS

Percent

TimeDelay

Level terrain Rolling terrain

AvgbSpeed

Percent no passing zones AvgbSpeed

Percent no passing zones AvgbSpeed0 20 40 60 80 100 0 20 40 60 80 100

A 30 94 0.15 0.12 0.09 0.07 0.05 0.04 92 0.15 0.10 0.07 0.05 0.04 0.03 90

B 45 89 0.27 0.24 0.21 0.19 0.17 0.16 87 0.26 0.23 0.19 0.17 0.15 0.13 87

C 60 84 0.43 0.39 0.36 0.34 0.33 0.32 82 0.42 0.39 0.35 0.32 0.30 0.28 79

D 75 81 0.64 0.62 0.60 0.59 0.58 0.57 79 0.62 0.57 0.52 0.48 0.46 0.43 73

E > 75 73 1.00 1.00 1.00 1.00 1.00 1.00 65 0.97 0.94 0.92 0.91 0.90 0.90 57

F 100 < 45 - - - - - -


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Table 2.4 Adjustment factors for directional distribution (fd) for two-lane highways

Directional

Distribution100/0 90/10 80/20 70/30 60/40 50/50

AdjustmentFactor

0.71 0.75 0.83 0.89 0.94 1.0

Source: Table 8-4, Highway Capacity Manual, Transport Research Board, National Research Council,Washington D.C., USA

Table 2.5 Adjustment factors for combined effect of narrow lanes and restricted

shoulder width (fw)

Usable

shoulderwidth

3.7 m lanes 3.4 m lanes 3.0 m lanes 2.7 m lanes

LOSA-D

LOSE

LOSA-D

LOSE

LOSA-D

LOSE

LOSA-D

LOSE

1.8 1.0 1.0 0.93 0.94 0.84 0.87 0.70 0.76

1.2 0.92 0.97 0.85 0.92 0.77 0.85 0.65 0.74

0.6 0.81 0.93 0.75 0.88 0.68 0.81 0.57 0.70

0 0.70 0.88 0.65 0.82 0.58 0.75 0.49 0.66

Note: where shoulder width is different on either side of the road use the average width

Source: Table 8-5, Highway Capacity Manual, Transport Research Board, National Research Council,

Washington D.C., USA

Table 2.6 Average passenger car equivalent for trucks and buses on two-lanehighways over different terrain segments

Vehicle Type LOSType of Terrain

Level Rolling Mountainous

Trucks ET

A 2.0 4.0 7.0

B & C 2.2 5.0 10.0

D & E 2.0 5.0 12.0

Buses EBA 1.8 3.0 5.7

B & C 2.0 3.4 5.7

D & E 1.6 2.9 6.5




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Table 2.7 Values of v/c ratiosa

vs speed, percent grade and percent no passing

zone for specific grades

Percent GradeAverage

Upgrade Speed (Kmph)

Percent no passing zones

0 20 40 60 80 100

3

89 0.27 0.23 0.19 0.17 0.14 0.12

85 0.42 0.38 0.33 0.31 0.29 0.2781 0.64 0.59 0.55 0.52 0.49 0.47

73 1.00 0.95 0.91 0.88 0.86 0.84

69 1.00 0.98 0.97 0.96 0.95 0.94

65 1.00 1.00 1.00 1.00 1.00 1.00

4

89 0.25 0.21 0.18 0.16 0.13 0.11

85 0.40 0.36 0.31 0.29 0.27 0.25

81 0.61 0.56 0.52 0.49 0.47 0.45

73 0.97 0.92 0.88 0.85 0.83 0.81

69 0.99 0.96 0.95 0.94 0.93 0.92

65 1.00 1.00 1.00 1.00 1.00 1.00

5

89 0.21 0.17 0.14 0.12 0.10 0.08

85 0.36 0.31 0.27 0.24 0.22 0.20

81 0.57 0.49 0.45 0.41 0.39 0.37

73 0.93 0.84 0.79 0.75 0.72 0.70

69 0.97 0.90 0.87 0.85 0.83 0.82

65 0.98 0.96 0.95 0.94 0.93 0.92

57 1.00 1.00 1.00 1.00 1.00 1.00

6

89 0.12 0.10 0.08 0.06 0.05 0.04

85 0.27 0.22 0.18 0.16 0.14 0.13

81 0.48 0.40 0.35 0.31 0.28 0.26

73 0.49 0.76 0.68 0.63 0.59 0.55

69 0.93 0.84 0.78 0.74 0.70 0.6765 0.97 0.91 0.87 0.83 0.81 0.78

57 1.00 0.96 0.95 0.93 0.91 0.90

49 1.00 0.99 0.99 0.98 0.98 0.98

7

89 0.00 0.00 0.00 0.00 0.00 0.00

85 0.13 0.10 0.08 0.07 0.05 0.04

81 0.34 0.27 0.22 0.18 0.15 0.12

73 0.77 0.65 0.55 0.46 0.40 0.35

69 0.86 0.75 0.67 0.60 0.54 0.48

65 0.93 0.82 0.75 0.69 0.64 0.59

57 1.00 0.91 0.87 0.82 0.79 0.76

49 1.00 0.95 0.92 0.90 0.88 0.86

a Ratio of flow rate to ideal capacity of 2800 pcph assuming car operation is unaffected by grade

Note: Interpolate for intermediate values of percent no passing zones round percent grade to the next

higher integer value



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Table 2.8 Adjustment factors for directional distribution for specific grades (fd)

Percent of Traffic on Upgrade Adjustment Factor (fd)

100 0.58

90 0.64

80 0.7070 0.78

60 0.87

50 1.00

40 1.20

30 1.50



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Table 2.9 Passenger car equivalent for specific grades

on two-lane highways E and E0

Grade % Length of grade

Meters

Average Upgrade Speed (kmph)

73 64 48

0 All 1.4 1.3 1.3

3

400 1.7 1.6 1.5800 2.0 1.8 1.7

1200 2.3 2.0 1.9

1600 2.6 2.3 2.1

2400 3.4 2.9 2.5

3200 4.6 3.7 2.9

4800 7.3 5.6 3.8

6400 11.3 7.7 4.9

4

400 1.8 1.7 1.6

800 2.2 2.0 1.9

1200 2.7 2.3 2.1

1600 3.2 2.7 2.4

2400 4.7 3.8 3.1

3200 6.9 5.3 3.8

4800 12.5 9.0 5.5

6400 22.8 13.8 7.4

5

400 2.0 1.8 1.7

800 2.5 2.2 2.0

1200 3.1 2.7 2.4

1600 4.0 3.3 2.8

2400 6.3 4.9 3.8

3200 10.2 7.5 4.8

4800 22.0 14.6 7.8

6400 55.0 25.0 11.5

6

400 2.1 1.9 1.8

800 2.8 2.4 2.2

1200 3.7 3.1 2.7

1600 4.9 4.0 3.3

2400 8.5 6.4 4.7

3200 15.3 10.7 6.3

4800 38.0 23.9 11.3

6400 90.0 45.0 18.1

7

400 2.2 2.0 1.9

800 3.2 2.7 2.4

1200 4.3 3.6 3.01600 6.1 4.8 3.8

2400 11.5 8.4 5.8

3200 22.8 15.4 8.2

4800 66.0 38.5 16.1

6400 A a 28.0

a - Speed not attainable on grade specified. Note: Round percent Grade to next higher integer value




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Table 2.10 Equivalent factors for different axle loads

Wheel Load

(single and dual)(10

3Kg)

Axle Load

(103

Kg)Equivalent Factor

1.5 3.0 0.012.0 4.0 0.04

2.5 5.0 0.11

3.0 6.0 0.25

3.5 7.0 0.50

4.0 8.0 0.91

4.5 9.0 1.55

5.0 10.0 2.50

5.5 11.0 3.83

6.0 12.0 5.67

6.5 13.0 8.13

7.0 14.0 11.37.5 15.0 15.5

8.0 16.0 20.7

8.5 17.0 27.2

9.0 18.0 35.2

9.5 19.0 44.9

10.0 20.0 56.5Source: Road Note 31, Fourth Edition 1993- Transport Research Laboratory, UK.


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3. Highway Capacity Design (HCM 2000)

f

VSFFS

HV

f

FM 0125.0+=

ffBFFSFFS ALS =

ffPHF

V

HVG

pv**

=

( ) ( )1111

++=

EPEPf

RRTT

HV


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fvFFSATS npp = 0125.0

fBPTSFPTSFnpd+=

( )e vBPTSF p000879.01100 =

c

vcv p=

LPHF

VVkmT t

= 25.015

LVVkmT t*60=


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ATS

VkmTTT

15

15 =

ffPHF

V

HVG

dv**

=

ffPHF

V

HVG

o

ov**

=

( ) ( ) ( ) ( )1111*11

+++=

EPEPPEPPf

RRTTC TTCTTC

HV


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( ) fvvFFSATS npoddd += 0125.0

fBPTSFPTSF npdd +=

= eav

BPTSFb

d

d 1100

( )LLLLL deplutd ++=

L

L

f

LfLLPTSFPTSF

t

de

pl

plpldud

pl

++++

=2

1


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( )

L

L

LfLfLfLPTSF

PTSFt

de

depl

deplplplud

pl

+++

=

2'

'

2

1

f

L

f

LLL

LATSATS

pl

de

pl

pl

du

tdpl

++++

=

1

2

*

( )

++

++

=

L

LLff

L

f

LL

LATSATS

de

dede

plpl

de

pl

pl

u

tdpl

'

'

11

2

*


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TTTTTT

PTSFTTPTSFTTPTSFTTPTSF

n

nnc

+++

+++=

...

*...**

21

2211

TTTTTT

VkmTVkmTVkmTATS

n

nc

+++

+++=

...

...

21

21


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4. TRAFFIC INCIDENT ANALYSISShock Wave Analysis

The velocity of a shock-wave that is created when the state of a traffic stream changes

from (qi, ki) to (qj, kj) is

ij

ij

ijkk

qqw

=

For forward and reverse shock-waveswij >0 and wij < 0 respectively.

Total delay

The total upstream delay is given by

)()( 1

3

2

1txAkk

i

ii=

whereAi (x,t) is the area in the (x,t) plane that has a density ki

The delay can also be computed when q2=0 to be equal to

( )1331

2

2 qq

qq

Where is the length of the incident

(when q2=0)


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5. TRAFFIC SIGNAL DESIGN SUMMARY1. Identify lane geometry2. Identify hourly volumes3. Calculate pedestrian crossing times (walking speed 1.0-1.5m/s)4. Calculate amber and all red times (reaction time- 1.0sec, Table 15)5. Check through plus right turns (assume 2 R.Ts during amber when separate

turning lane is available)

Gi +Ii) calculate new cycle time based onnew Gi + Iis. Recalculate effective green times.

16.Calculate green and red times.

Table 11 Right turn equivalencies

1.Right turn lane available 1 R.T. = 1.05 through

2. Right turn lane not available

Opposing Volume/Hour 0-299 300-599 600-999 >1000i. No separate turn phase

equivalent through per R.T.1.2 2.0 4.0 6.0

ii. Separate turn phase 1.2 1.2 1.2 1.2

Reference: TRB (1980)

Table 12 Right and left turning movement multiplicative factors

Pedestrian Flow per Hour Multiplicative Factor

Low 0-99 1.00

Moderate 100-599 1.25

Heavy 600-1199 1.50Very Heavy > 1200 2.00


Table 13 Lane width adjustment factors

Lane Width Multiplicative Factor

2.45 3.00 m 1.10

3.05 3.95 m 1.00

3.97 4.85 m 0.90

4.88 5.76 m 0.80


>

7

4=

10cycleperpedestrianifsec

10cycleperpedestrianifsec


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Table 14 Level of Service

Maximum Sum of Critical Lane Volumes

Level of Service Two Phase Three Phase Four or more

Phases

A 1000 950 900

B 1200 1140 1080C 1400 1340 1270

D 1600 1530 1460

E 1800 1720 1650


Table 15 Minimum amber periods

Speed Limit

(km/hr)

Minimum Amber Period

(sec.)

VL 50 3

50 < VL 60 4

60 < VL 70 570 < VL 80 6


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6. Geometric Design EquationsStopping Sight Distance (SSD)

2546.3

2

VVtSSD R +=

Where,

SSD is the Stopping Sight Distance in meters

V is the Design Speed of the vehicle in km/h

tRis the total Reaction Time

is the coefficient of friction

Minimum Radius of a Horizontal Curve

( )maxmax

2

min127 fe

VR

+=

Critical Conditions,

Sliding;

( )feV

R+

=127

2

Overturning;

( )H

Te

VR

2127

2

+=

For Vertical Curves

Length of Curve (L)Sight Distance (S)

C

ASL

2

=

C, a constant for crest curves

[ ]221200 hhC +=


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7. MARSHALL MIX DESIGN CRITERIATable 1 Minimum VMA requirement

Nominal Maximum Particle Size Minimum VMA(mm) (U.S.) (percent)

63 2.5 inch 11

50 2.0 inch 11.5

37.5 1.5 inch 12

25 1.0 inch 13

19 0.75 inch 14

12.5 0.5 inch 15

9.5 0.375 inch 16

4.75 No. 4 sieve 18

2.36 No. 8 sieve 21

1.18 No. 16 sieve 23.5

Table 2 Mix Design Criteria

Mix Criteria Light Traffic

(106 ESALS)

min max min max min max

Compaction

(number of blows oneach end of the sample)

35 50 75

Stability (minimum)2224 N

(500 lbs.)

3336 N

(750 lbs.)

6672 N

(1500 lbs.)

Flow (0.25mm/0.01inch) 8 20 8 18 8 16

Percent air voids 3 5 3 5 3 5


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Chapter 5 Roadway Design

2 Page Revised: 10/21/2008

Figure 1: Design chart for flexible pavements based on using mean values for each input

AASHTO Guide for Design of Pavement Structures, 1993


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Determination of Layer Thicknesses

1

11

a

SND

22

122

ma

SNSND

( )

33

213

3ma

SNSNSND

+

D1

D2

D3SN3

SN2

SN1

Roadbed Course

Surface Course

Base Course

Subbase Course


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Structural Coefficients

Layer Structural Coefficient

Single Surface Dressing 0.1

Sand Seal, hot bitumen application 0.05-0.01

DBST 0.2

Asphalt concrete (high stability) 0.4

Hot rolled asphalt (surfacing) 0.35-0.40

Flexible bituminous surfacing 0.3

Bitumen macadam road base 0.3

Bitumen bound base, Asphalt treated base 0.3

Penetration macadam 0.2

Dense graded crushed stone base (CBR 110) 0.14

Water bound and dry bound macadam 0.14

Single sized aggregate base 0.125

Granular base (CBR 80) 0.12

Granular base (CBR 30) 0.11

Granular sub base (CBR 20) 0.095

Capping layer (CBR 15) 0.09

Granular sub base/ Capping layer (CBR8) 0.07

Source: AASHTO 1993


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KEY TO STRUCTURAL CATALOGUE


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CHART 1 GRANULAR ROADBASE / SURFACE DRESSING


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CHART 2 COMPOSITE ROAD BASE (UNBOUND & CEMENTED) / SURFACE DRESSING


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CHART 3 GRANULAR ROADBASE / SEMI-STRUCTURAL SURFACE


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CHART 4 COMPOSITE ROADBASE / SEMI - STRUCTURAL SURFACE


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CHART 5 GRANULAR ROADBASE / STRUCTURAL SURFACE


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CHART 6 COMPOSITE ROADBASE / STRUCTURAL SURFACE


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CHART 7 BITUMINOUS ROADBASE / SEMI-STRUCTURAL SURFACE


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CHART 8 CEMENTED ROADBASE / SURFACE DRESSING


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z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002

-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003

-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005

-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007

-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010

-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014

-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019

-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026

-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036

-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048

-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064

-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084

-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110

-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143

-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183

-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233

-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294

-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367

-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455

-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559

-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681

-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823

-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985

-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170

-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379

-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611

-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867

-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148

-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451

-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776

-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483

-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859

-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247

0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641

Standard Normal Cumulative Probability Table

Cumulative probabilities for NEGATIVE z-values are shown in the following table:


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z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890

2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993

3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995

3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

Standard Normal Cumulative Probability Table

Cumulative probabilities for POSITIVE z-values are shown in the following table:


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Statistical Tables for Students Binomial

Table 1 Binomial distrib ution prob ability fun ction

p

x 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

n=1 0 .9900 .9500 .9000 .8500 .8000 .7500 .7000 .6500 .6000 .5500 .5000 1

1 .0100 .0500 .1000 .1500 .2000 .2500 .3000 .3500 .4000 .4500 .5000 0

n=2 0 .9801 .9025 .8100 .7225 .6400 .5625 .4900 .4225 .3600 .3025 .2500 2

1 .0198 .0950 .1800 .2550 .3200 .3750 .4200 .4550 .4800 .4950 .5000 1

2 .0001 .0025 .0100 .0225 .0400 .0625 .0900 .1225 .1600 .2025 .2500 0

n=3 0 .9703 .8574 .7290 .6141 .5120 .4219 .3430 .2746 .2160 .1664 .1250 3

1 .0294 .1354 .2430 .3251 .3840 .4219 .4410 .4436 .4320 .4084 .3750 2

2 .0003 .0071 .0270 .0574 .0960 .1406 .1890 .2389 .2880 .3341 .3750 1

3 .0001 .0010 .0034 .0080 .0156 .0270 .0429 .0640 .0911 .1250 0

n=4 0 .9606 .8145 .6561 .5220 .4096 .3164 .2401 .1785 .1296 .0915 .0625 4

1 .0388 .1715 .2916 .3685 .4096 .4219 .4116 .3845 .3456 .2995 .2500 32 .0006 .0135 .0486 .0975 .1536 .2109 .2646 .3105 .3456 .3675 .3750 2

3 .0005 .0036 .0115 .0256 .0469 .0756 .1115 .1536 .2005 .2500 1

4 .0001 .0005 .0016 .0039 .0081 .0150 .0256 .0410 .0625 0

n=5 0 .9510 .7738 .5905 .4437 .3277 .2373 .1681 .1160 .0778 .0503 .0313 5

1 .0480 .2036 .3281 .3915 .4096 .3955 .3602 .3124 .2592 .2059 .1563 4

2 .0010 .0214 .0729 .1382 .2048 .2637 .3087 .3364 .3456 .3369 .3125 3

3 .0011 .0081 .0244 .0512 .0879 .1323 .1811 .2304 .2757 .3125 2

4 .0005 .0022 .0064 .0146 .0284 .0488 .0768 .1128 .1563 1

5 .0001 .0003 .0010 .0024 .0053 .0102 .0185 .0313 0

n=6 0 .9415 .7351 .5314 .3771 .2621 .1780 .1176 .0754 .0467 .0277 .0156 6

1 .0571 .2321 .3543 .3993 .3932 .3560 .3025 .2437 .1866 .1359 .0938 5

2 .0014 .0305 .0984 .1762 .2458 .2966 .3241 .3280 .3110 .2780 .2344 4

3 .0021 .0146 .0415 .0819 .1318 .1852 .2355 .2765 .3032 .3125 34 .0001 .0012 .0055 .0154 .0330 .0595 .0951 .1382 .1861 .2344 2

5 .0001 .0004 .0015 .0044 .0102 .0205 .0369 .0609 .0938 1

6 .0001 .0002 .0007 .0018 .0041 .0083 .0156 0

n=7 0 .9321 .6983 .4783 .3206 .2097 .1335 .0824 .0490 .0280 .0152 .0078 7

1 .0659 .2573 .3720 .3960 .3670 .3115 .2471 .1848 .1306 .0872 .0547 6

2 .0020 .0406 .1240 .2097 .2753 .3115 .3177 .2985 .2613 .2140 .1641 5

3 .0036 .0230 .0617 .1147 .1730 .2269 .2679 .2903 .2918 .2734 4

4 .0002 .0026 .0109 .0287 .0577 .0972 .1442 .1935 .2388 .2734 3

5 .0002 .0012 .0043 .0115 .0250 .0466 .0774 .1172 .1641 2

6 .0001 .0004 .0013 .0036 .0084 .0172 .0320 .0547 1

7 .0001 .0002 .0006 .0016 .0037 .0078 0

n=8 0 .9227 .6634 .4305 .2725 .1678 .1001 .0576 .0319 .0168 .0084 .0039 8

1 .0746 .2793 .3826 .3847 .3355 .2670 .1977 .1373 .0896 .0548 .0313 72 .0026 .0515 .1488 .2376 .2936 .3115 .2965 .2587 .2090 .1569 .1094 6

3 .0001 .0054 .0331 .0839 .1468 .2076 .2541 .2786 .2787 .2568 .2188 5

4 .0004 .0046 .0185 .0459 .0865 .1361 .1875 .2322 .2627 .2734 4

5 .0004 .0026 .0092 .0231 .0467 .0808 .1239 .1719 .2188 3

6 .0002 .0011 .0038 .0100 .0217 .0413 .0703 .1094 2

7 .0001 .0004 .0012 .0033 .0079 .0164 .0313 1

8 .0001 .0002 .0007 .0017 .0039 0

0.99 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xp


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p

x 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

n=9 0 0.9135 0.6302 0.3874 0.2316 0.1342 0.0751 0.0404 0.0207 0.0101 0.0046 0.0020 9

1 0.0830 0.2985 0.3874 0.3679 0.3020 0.2253 0.1556 0.1004 0.0605 0.0339 0.0176 8

2 0.0034 0.0629 0.1722 0.2597 0.3020 0.3003 0.2668 0.2162 0.1612 0.1110 0.0703 7

3 0.0001 0.0077 0.0446 0.1069 0.1762 0.2336 0.2668 0.2716 0.2508 0.2119 0.1641 6

4 0.0006 0.0074 0.0283 0.0661 0.1168 0.1715 0.2194 0.2508 0.2600 0.2461 55 0.0008 0.0050 0.0165 0.0389 0.0735 0.1181 0.1672 0.2128 0.2461 4

6 0.0001 0.0006 0.0028 0.0087 0.0210 0.0424 0.0743 0.1160 0.1641 3

7 0.0003 0.0012 0.0039 0.0098 0.0212 0.0407 0.0703 2

8 0.0001 0.0004 0.0013 0.0035 0.0083 0.0176 1

9 0.0001 0.0003 0.0008 0.0020 0

n=10 0 0.9044 0.5987 0.3487 0.1969 0.1074 0.0563 0.0282 0.0135 0.0060 0.0025 0.0010 10

1 0.0914 0.3151 0.3874 0.3474 0.2684 0.1877 0.1211 0.0725 0.0403 0.0207 0.0098 9

2 0.0042 0.0746 0.1937 0.2759 0.3020 0.2816 0.2335 0.1757 0.1209 0.0763 0.0439 8

3 0.0001 0.0105 0.0574 0.1298 0.2013 0.2503 0.2668 0.2522 0.2150 0.1665 0.1172 7

4 0.0010 0.0112 0.0401 0.0881 0.1460 0.2001 0.2377 0.2508 0.2384 0.2051 6

5 0.0001 0.0015 0.0085 0.0264 0.0584 0.1029 0.1536 0.2007 0.2340 0.2461 5

6 0.0001 0.0012 0.0055 0.0162 0.0368 0.0689 0.1115 0.1596 0.2051 4

7 0.0001 0.0008 0.0031 0.0090 0.0212 0.0425 0.0746 0.1172 3

8 0.0001 0.0004 0.0014 0.0043 0.0106 0.0229 0.0439 29 0.0001 0.0005 0.0016 0.0042 0.0098 1

10 0.0001 0.0003 0.0010 0

n=11 0 0.8953 0.5688 0.3138 0.1673 0.0859 0.0422 0.0198 0.0088 0.0036 0.0014 0.0005 11

1 0.0995 0.3293 0.3835 0.3248 0.2362 0.1549 0.0932 0.0518 0.0266 0.0125 0.0054 10

2 0.0050 0.0867 0.2131 0.2866 0.2953 0.2581 0.1998 0.1395 0.0887 0.0513 0.0269 9

3 0.0002 0.0137 0.0710 0.1517 0.2215 0.2581 0.2568 0.2254 0.1774 0.1259 0.0806 8

4 0.0014 0.0158 0.0536 0.1107 0.1721 0.2201 0.2428 0.2365 0.2060 0.1611 7

5 0.0001 0.0025 0.0132 0.0388 0.0803 0.1321 0.1830 0.2207 0.2360 0.2256 6

6 0.0003 0.0023 0.0097 0.0268 0.0566 0.0985 0.1471 0.1931 0.2256 5

7 0.0003 0.0017 0.0064 0.0173 0.0379 0.0701 0.1128 0.1611 4

8 0.0002 0.0011 0.0037 0.0102 0.0234 0.0462 0.0806 3

9 0.0001 0.0005 0.0018 0.0052 0.0126 0.0269 2

10 0.0002 0.0007 0.0021 0.0054 1

11 0.0002 0.0005 0

n=12 0 0.8864 0.5404 0.2824 0.1422 0.0687 0.0317 0.0138 0.0057 0.0022 0.0008 0.0002 12

1 0.1074 0.3413 0.3766 0.3012 0.2062 0.1267 0.0712 0.0368 0.0174 0.0075 0.0029 11

2 0.0060 0.0988 0.2301 0.2924 0.2835 0.2323 0.1678 0.1088 0.0639 0.0339 0.0161 10

3 0.0002 0.0173 0.0852 0.1720 0.2362 0.2581 0.2397 0.1954 0.1419 0.0923 0.0537 9

4 0.0021 0.0213 0.0683 0.1329 0.1936 0.2311 0.2367 0.2128 0.1700 0.1208 8

5 0.0002 0.0038 0.0193 0.0532 0.1032 0.1585 0.2039 0.2270 0.2225 0.1934 7

6 0.0005 0.0040 0.0155 0.0401 0.0792 0.1281 0.1766 0.2124 0.2256 6

7 0.0006 0.0033 0.0115 0.0291 0.0591 0.1009 0.1489 0.1934 5

8 0.0001 0.0005 0.0024 0.0078 0.0199 0.0420 0.0762 0.1208 4

9 0.0001 0.0004 0.0015 0.0048 0.0125 0.0277 0.0537 3

10 0.0002 0.0008 0.0025 0.0068 0.0161 2

11 0.0001 0.0003 0.0010 0.0029 1

12 0.0001 0.0002 0

n=13 0 0.8775 0.5133 0.2542 0.1209 0.0550 0.0238 0.0097 0.0037 0.0013 0.0004 0.0001 13

1 0.1152 0.3512 0.3672 0.2774 0.1787 0.1029 0.0540 0.0259 0.0113 0.0045 0.0016 12

2 0.0070 0.1109 0.2448 0.2937 0.2680 0.2059 0.1388 0.0836 0.0453 0.0220 0.0095 11

3 0.0003 0.0214 0.0997 0.1900 0.2457 0.2517 0.2181 0.1651 0.1107 0.0660 0.0349 10

4 0.0028 0.0277 0.0838 0.1535 0.2097 0.2337 0.2222 0.1845 0.1350 0.0873 9

5 0.0003 0.0055 0.0266 0.0691 0.1258 0.1803 0.2154 0.2214 0.1989 0.1571 8

6 0.0008 0.0063 0.0230 0.0559 0.1030 0.1546 0.1968 0.2169 0.2095 7

7 0.0001 0.0011 0.0058 0.0186 0.0442 0.0833 0.1312 0.1775 0.2095 6

8 0.0001 0.0011 0.0047 0.0142 0.0336 0.0656 0.1089 0.1571 5

9 0.0001 0.0009 0.0034 0.0101 0.0243 0.0495 0.0873 4

10 0.0001 0.0006 0.0022 0.0065 0.0162 0.0349 3

11 0.0001 0.0003 0.0012 0.0036 0.0095 2

12 0.0001 0.0005 0.0016 1

13 0.0001 0

0.99 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 x

p


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p

x 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

n=14 0 0.8687 0.4877 0.2288 0.1028 0.0440 0.0178 0.0068 0.0024 0.0008 0.0002 0.0001 14

1 0.1229 0.3593 0.3559 0.2539 0.1539 0.0832 0.0407 0.0181 0.0073 0.0027 0.0009 13

2 0.0081 0.1229 0.2570 0.2912 0.2501 0.1802 0.1134 0.0634 0.0317 0.0141 0.0056 12

3 0.0003 0.0259 0.1142 0.2056 0.2501 0.2402 0.1943 0.1366 0.0845 0.0462 0.0222 11

4 0.0037 0.0349 0.0998 0.1720 0.2202 0.2290 0.2022 0.1549 0.1040 0.0611 10

5 0.0004 0.0078 0.0352 0.0860 0.1468 0.1963 0.2178 0.2066 0.1701 0.1222 9

6 0.0013 0.0093 0.0322 0.0734 0.1262 0.1759 0.2066 0.2088 0.1833 8

7 0.0002 0.0019 0.0092 0.0280 0.0618 0.1082 0.1574 0.1952 0.2095 7

8 0.0003 0.0020 0.0082 0.0232 0.0510 0.0918 0.1398 0.1833 6

9 0.0003 0.0018 0.0066 0.0183 0.0408 0.0762 0.1222 5

10 0.0003 0.0014 0.0049 0.0136 0.0312 0.0611 4

11 0.0002 0.0010 0.0033 0.0093 0.0222 3

12 0.0001 0.0005 0.0019 0.0056 2

13 0.0001 0.0002 0.0009 1

14 0.0001 0

n=15 0 0.8601 0.4633 0.2059 0.0874 0.0352 0.0134 0.0047 0.0016 0.0005 0.0001 15

1 0.1303 0.3658 0.3432 0.2312 0.1319 0.0668 0.0305 0.0126 0.0047 0.0016 0.0005 14

2 0.0092 0.1348 0.2669 0.2856 0.2309 0.1559 0.0916 0.0476 0.0219 0.0090 0.0032 13

3 0.0004 0.0307 0.1285 0.2184 0.2501 0.2252 0.1700 0.1110 0.0634 0.0318 0.0139 12

4 0.0049 0.0428 0.1156 0.1876 0.2252 0.2186 0.1792 0.1268 0.0780 0.0417 11

5 0.0006 0.0105 0.0449 0.1032 0.1651 0.2061 0.2123 0.1859 0.1404 0.0916 106 0.0019 0.0132 0.0430 0.0917 0.1472 0.1906 0.2066 0.1914 0.1527 9

7 0.0003 0.0030 0.0138 0.0393 0.0811 0.1319 0.1771 0.2013 0.1964 8

8 0.0005 0.0035 0.0131 0.0348 0.0710 0.1181 0.1647 0.1964 7

9 0.0001 0.0007 0.0034 0.0116 0.0298 0.0612 0.1048 0.1527 6

10 0.0001 0.0007 0.0030 0.0096 0.0245 0.0515 0.0916 5

11 0.0001 0.0006 0.0024 0.0074 0.0191 0.0417 4

12 0.0001 0.0004 0.0016 0.0052 0.0139 3

13 0.0001 0.0003 0.0010 0.0032 2

14 0.0001 0.0005 1

15 0

n=16 0 0.8515 0.4401 0.1853 0.0743 0.0281 0.0100 0.0033 0.0010 0.0003 0.0001 16

1 0.1376 0.3706 0.3294 0.2097 0.1126 0.0535 0.0228 0.0087 0.0030 0.0009 0.0002 15

2 0.0104 0.1463 0.2745 0.2775 0.2111 0.1336 0.0732 0.0353 0.0150 0.0056 0.0018 14

3 0.0005 0.0359 0.1423 0.2285 0.2463 0.2079 0.1465 0.0888 0.0468 0.0215 0.0085 13

4 0.0061 0.0514 0.1311 0.2001 0.2252 0.2040 0.1553 0.1014 0.0572 0.0278 12

5 0.0008 0.0137 0.0555 0.1201 0.1802 0.2099 0.2008 0.1623 0.1123 0.0667 11

6 0.0001 0.0028 0.0180 0.0550 0.1101 0.1649 0.1982 0.1983 0.1684 0.1222 10

7 0.0004 0.0045 0.0197 0.0524 0.1010 0.1524 0.1889 0.1969 0.1746 9

8 0.0001 0.0009 0.0055 0.0197 0.0487 0.0923 0.1417 0.1812 0.1964 8

9 0.0001 0.0012 0.0058 0.0185 0.0442 0.0840 0.1318 0.1746 7

10 0.0002 0.0014 0.0056 0.0167 0.0392 0.0755 0.1222 6

11 0.0002 0.0013 0.0049 0.0142 0.0337 0.0667 5

12 0.0002 0.0011 0.0040 0.0115 0.0278 4

13 0.0000 0.0002 0.0008 0.0029 0.0085 3

14 0.0001 0.0005 0.0018 2

15 0.0001 0.0002 1

16 0

n=17 0 0.8429 0.4181 0.1668 0.0631 0.0225 0.0075 0.0023 0.0007 0.0002 17

1 0.1447 0.3741 0.3150 0.1893 0.0957 0.0426 0.0169 0.0060 0.0019 0.0005 0.0001 16

2 0.0117 0.1575 0.2800 0.2673 0.1914 0.1136 0.0581 0.0260 0.0102 0.0035 0.0010 15

3 0.0006 0.0415 0.1556 0.2359 0.2393 0.1893 0.1245 0.0701 0.0341 0.0144 0.0052 14

4 0.0076 0.0605 0.1457 0.2093 0.2209 0.1868 0.1320 0.0796 0.0411 0.0182 13

5 0.0010 0.0175 0.0668 0.1361 0.1914 0.2081 0.1849 0.1379 0.0875 0.0472 12

6 0.0001 0.0039 0.0236 0.0680 0.1276 0.1784 0.1991 0.1839 0.1432 0.0944 11

7 0.0007 0.0065 0.0267 0.0668 0.1201 0.1685 0.1927 0.1841 0.1484 10

8 0.0001 0.0014 0.0084 0.0279 0.0644 0.1134 0.1606 0.1883 0.1855 9

9 0.0003 0.0021 0.0093 0.0276 0.0611 0.1070 0.1540 0.1855 8

10 0.0004 0.0025 0.0095 0.0263 0.0571 0.1008 0.1484 7

11 0.0001 0.0005 0.0026 0.0090 0.0242 0.0525 0.0944 6

12 0.0001 0.0006 0.0024 0.0081 0.0215 0.0472 5

13 0.0001 0.0005 0.0021 0.0068 0.0182 4

14 0.0001 0.0004 0.0016 0.0052 3

15 0.0001 0.0003 0.0010 2

16 0.0001 1

17 0

0.99 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xp


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p

x 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

n=18 0 0.8345 0.3972 0.1501 0.0536 0.0180 0.0056 0.0016 0.0004 0.0001 18

1 0.1517 0.3763 0.3002 0.1704 0.0811 0.0338 0.0126 0.0042 0.0012 0.0003 0.0001 17

2 0.0130 0.1683 0.2835 0.2556 0.1723 0.0958 0.0458 0.0190 0.0069 0.0022 0.0006 16

3 0.0007 0.0473 0.1680 0.2406 0.2297 0.1704 0.1046 0.0547 0.0246 0.0095 0.0031 15

4 0.0093 0.0700 0.1592 0.2153 0.2130 0.1681 0.1104 0.0614 0.0291 0.0117 14

5 0.0014 0.0218 0.0787 0.1507 0.1988 0.2017 0.1664 0.1146 0.0666 0.0327 13

6 0.0002 0.0052 0.0301 0.0816 0.1436 0.1873 0.1941 0.1655 0.1181 0.0708 12

7 0.0010 0.0091 0.0350 0.0820 0.1376 0.1792 0.1892 0.1657 0.1214 11

8 0.0002 0.0022 0.0120 0.0376 0.0811 0.1327 0.1734 0.1864 0.1669 10

9 0.0004 0.0033 0.0139 0.0386 0.0794 0.1284 0.1694 0.1855 9

10 0.0001 0.0008 0.0042 0.0149 0.0385 0.0771 0.1248 0.1669 8

11 0.0001 0.0010 0.0046 0.0151 0.0374 0.0742 0.1214 7

12 0.0002 0.0012 0.0047 0.0145 0.0354 0.0708 6

13 0.0002 0.0012 0.0045 0.0134 0.0327 5

14 0.0002 0.0011 0.0039 0.0117 4

15 0.0002 0.0009 0.0031 3

16 0.0001 0.0006 2

17 0.0001 1

18 0

n=19 0 0.8262 0.3774 0.1351 0.0456 0.0144 0.0042 0.0011 0.0003 0.0001 19

1 0.1586 0.3774 0.2852 0.1529 0.0685 0.0268 0.0093 0.0029 0.0008 0.0002 18

2 0.0144 0.1787 0.2852 0.2428 0.1540 0.0803 0.0358 0.0138 0.0046 0.0013 0.0003 17

3 0.0008 0.0533 0.1796 0.2428 0.2182 0.1517 0.0869 0.0422 0.0175 0.0062 0.0018 16

4 0.0112 0.0798 0.1714 0.2182 0.2023 0.1491 0.0909 0.0467 0.0203 0.0074 15

5 0.0018 0.0266 0.0907 0.1636 0.2023 0.1916 0.1468 0.0933 0.0497 0.0222 14

6 0.0002 0.0069 0.0374 0.0955 0.1574 0.1916 0.1844 0.1451 0.0949 0.0518 13

7 0.0014 0.0122 0.0443 0.0974 0.1525 0.1844 0.1797 0.1443 0.0961 12

8 0.0002 0.0032 0.0166 0.0487 0.0981 0.1489 0.1797 0.1771 0.1442 11

9 0.0007 0.0051 0.0198 0.0514 0.0980 0.1464 0.1771 0.1762 10

10 0.0001 0.0013 0.0066 0.0220 0.0528 0.0976 0.1449 0.1762 9

11 0.0003 0.0018 0.0077 0.0233 0.0532 0.0970 0.1442 8

12 0.0004 0.0022 0.0083 0.0237 0.0529 0.0961 7

13 0.0001 0.0005 0.0024 0.0085 0.0233 0.0518 6

14 0.0001 0.0006 0.0024 0.0082 0.0222 5

15 0.0001 0.0005 0.0022 0.0074 4

16 0.0001 0.0005 0.0018 3

17 0.0001 0.0003 2

18 1

19 0

n=20 0 0.8179 0.3585 0.1216 0.0388 0.0115 0.0032 0.0008 0.0002 20

1 0.1652 0.3774 0.2702 0.1368 0.0576 0.0211 0.0068 0.0020 0.0005 0.0001 19

2 0.0159 0.1887 0.2852 0.2293 0.1369 0.0669 0.0278 0.0100 0.0031 0.0008 0.0002 18

3 0.0010 0.0596 0.1901 0.2428 0.2054 0.1339 0.0716 0.0323 0.0123 0.0040 0.0011 17

4 0.0133 0.0898 0.1821 0.2182 0.1897 0.1304 0.0738 0.0350 0.0139 0.0046 16

5 0.0022 0.0319 0.1028 0.1746 0.2023 0.1789 0.1272 0.0746 0.0365 0.0148 15

6 0.0003 0.0089 0.0454 0.1091 0.1686 0.1916 0.1712 0.1244 0.0746 0.0370 14

7 0.0020 0.0160 0.0545 0.1124 0.1643 0.1844 0.1659 0.1221 0.0739 13

8 0.0004 0.0046 0.0222 0.0609 0.1144 0.1614 0.1797 0.1623 0.1201 12

9 0.0001 0.0011 0.0074 0.0271 0.0654 0.1158 0.1597 0.1771 0.1602 11

10 0.0002 0.0020 0.0099 0.0308 0.0686 0.1171 0.1593 0.1762 10

11 0.0005 0.0030 0.0120 0.0336 0.0710 0.1185 0.1602 9

12 0.0001 0.0008 0.0039 0.0136 0.0355 0.0727 0.1201 8

13 0.0002 0.0010 0.0045 0.0146 0.0366 0.0739 7

14 0.0002 0.0012 0.0049 0.0150 0.0370 6

15 0.0003 0.0013 0.0049 0.0148 5

16 0.0003 0.0013 0.0046 4

17 0.0002 0.0011 3

18 0.0002 2

19 1

20 0

0.99 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 x

p


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Poisson Probability Sums:

r 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.9048 0.8187 0.7788 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066

1 0.9953 0.9825 0.9735 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088 0.7725

2 0.9998 0.9989 0.9978 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.9371

3 1.0000 0.9999 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.9865

4 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977

5 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.99976 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

r 1 1.5 2 2.5 3 3.5 4 4.5 5

0 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.0067

1 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404

2 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.1247

3 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650

4 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405

5 0.9994 0.9955 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.6160

6 0.9999 0.9991 0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.7622

7 1.0000 0.9998 0.9989 0.9958 0.9881 0.9733 0.9489 0.9134 0.8666

8 1.0000 0.9998 0.9989 0.9962 0.9901 0.9786 0.9597 0.9319

9 1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.968210 0.9999 0.9997 0.9990 0.9972 0.9933 0.9863

11 1.0000 0.9999 0.9997 0.9991 0.9976 0.9945

12 1.0000 0.9999 0.9997 0.9992 0.9980

13 1.0000 0.9999 0.9997 0.9993

14 1.0000 0.9999 0.9998

15 1.0000 0.9999

16 1.0000

r 5.5 6 6.5 7 7.5 8 8.5 9 9.5

0 0.0041 0.0025 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0.0001

1 0.0266 0.0174 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 0.0008

2 0.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 0.0042

3 0.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0.0149

4 0.3575 0.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 0.0403

5 0.5289 0.4457 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.0885

6 0.6860 0.6063 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.1649

7 0.8095 0.7440 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.2687

8 0.8944 0.8472 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.3918

9 0.9462 0.9161 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.5218

10 0.9747 0.9574 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.6453

11 0.9890 0.9799 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.7520

12 0.9955 0.9912 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.8364

13 0.9983 0.9964 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.8981

14 0.9994 0.9986 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.9400

15 0.9998 0.9995 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.966516 0.9999 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823

17 1.0000 0.9999 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911

18 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957

19 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980

20 1.0000 0.9999 0.9998 0.9996 0.9991

21 1.0000 0.9999 0.9998 0.9996

22 1.0000 0.9999 0.9999

23 1.0000 0.9999

24 1.0000

=

r

x

xp

0

);(


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r 10 11 12 13 14 15 16 17 18

0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 0.0028 0.0012 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000

3 0.0103 0.0049 0.0023 0.0011 0.0005 0.0002 0.0001 0.0000 0.0000

4 0.0293 0.0151 0.0076 0.0037 0.0018 0.0009 0.0004 0.0002 0.0001

5 0.0671 0.0375 0.0203 0.0107 0.0055 0.0028 0.0014 0.0007 0.0003

6 0.1301 0.0786 0.0458 0.0259 0.0142 0.0076 0.0040 0.0021 0.0010

7 0.2202 0.1432 0.0895 0.0540 0.0316 0.0180 0.0100 0.0054 0.0029

8 0.3328 0.2320 0.1550 0.0998 0.0621 0.0374 0.0220 0.0126 0.00719 0.4579 0.3405 0.2424 0.1658 0.1094 0.0699 0.0433 0.0261 0.0154

10 0.5830 0.4599 0.3472 0.2517 0.1757 0.1185 0.0774 0.0491 0.0304

11 0.6968 0.5793 0.4616 0.3532 0.2600 0.1848 0.1270 0.0847 0.0549

12 0.7916 0.6887 0.5760 0.4631 0.3585 0.2676 0.1931 0.1350 0.0917

13 0.8645 0.7813 0.6815 0.5730 0.4644 0.3632 0.2745 0.2009 0.1426

14 0.9165 0.8540 0.7720 0.6751 0.5704 0.4657 0.3675 0.2808 0.2081

15 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681 0.4667 0.3715 0.2867

16 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641 0.5660 0.4677 0.3751

17 0.9857 0.9678 0.9370 0.8905 0.8272 0.7489 0.6593 0.5640 0.4686

18 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195 0.7423 0.6550 0.5622

19 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752 0.8122 0.7363 0.6509

20 0.9984 0.9953 0.9884 0.9750 0.9521 0.9170 0.8682 0.8055 0.730721 0.9993 0.9977 0.9939 0.9859 0.9712 0.9469 0.9108 0.8615 0.7991

22 0.9997 0.9990 0.9970 0.9924 0.9833 0.9673 0.9418 0.9047 0.8551

23 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805 0.9633 0.9367 0.8989

24 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888 0.9777 0.9594 0.9317

25 0.9999 0.9997 0.9990 0.9974 0.9938 0.9869 0.9748 0.9554

26 1.0000 0.9999 0.9995 0.9987 0.9967 0.9925 0.9848 0.9718

27 0.9999 0.9998 0.9994 0.9983 0.9959 0.9912 0.9827

28 1.0000 0.9999 0.9997 0.9991 0.9978 0.9950 0.9897

29 1.0000 0.9999 0.9996 0.9989 0.9973 0.9941

30 0.9999 0.9998 0.9994 0.9986 0.9967

31 1.0000 0.9999 0.9997 0.9993 0.9982

32 1.0000 0.9999 0.9996 0.9990

33 0.9999 0.9998 0.9995

34 1.0000 0.9999 0.9998

35 1.0000 0.9999

36 0.9999

37 1.0000


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Chi-Square Distribution Table

20

The shaded area is equal to for 2 = 2

.

df 2.995

2.990

2.975

2.950

2.900

2.100

2.050

2.025

2.010

2.005

1 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879

2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597

3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.8384 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860

5 0.412 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 16.750

6 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548

7 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278

8 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955

9 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589

10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188

11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757

12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300

13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.819

14 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.319

15 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801

16 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 34.26717 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 35.718

18 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37.156

19 6.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.582

20 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 39.997

21 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 41.401

22 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.796

23 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.181

24 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 45.559

25 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 46.928

26 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.290

27 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.645

28 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50.993

29 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 52.336

30 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672

40 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.766

50 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.420 76.154 79.490

60 35.534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952

70 43.275 45.442 48.758 51.739 55.329 85.527 90.531 95.023 100.425 104.215

80 51.172 53.540 57.153 60.391 64.278 96.578 101.879 106.629 112.329 116.321

90 59.196 61.754 65.647 69.126 73.291 107.565 113.145 118.136 124.116 128.299

100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169


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d.f. 0.40 0.25 0.10 0.05 0.04 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005

1 0.325 1.000 3.078 6.314 7.916 12.706 15.894 31.821 63.656 127.321 318.289 636.578

2 0.289 0.816 1.886 2.920 3.320 4.303 4.849 6.965 9.925 14.089 22.328 31.600

30.277 0.765 1.638 2.353 2.605 3.182 3.482 4.541 5.841 7.453 10.214 12.924

4 0.271 0.741 1.533 2.132 2.333 2.776 2.999 3.747 4.604 5.598 7.173 8.610

5 0.267 0.727 1.476 2.015 2.191 2.571 2.757 3.365 4.032 4.773 5.894 6.869

6 0.265 0.718 1.440 1.943 2.104 2.447 2.612 3.143 3.707 4.317 5.208 5.959

7 0.263 0.711 1.415 1.895 2.046 2.365 2.517 2.998 3.499 4.029 4.785 5.408

8 0.262 0.706 1.397 1.860 2.004 2.306 2.449 2.896 3.355 3.833 4.501 5.041

9 0.261 0.703 1.383 1.833 1.973 2.262 2.398 2.821 3.250 3.690 4.297 4.781

10 0.260 0.700 1.372 1.812 1.948 2.228 2.359 2.764 3.169 3.581 4.144 4.587

11 0.260 0.697 1.363 1.796 1.928 2.201 2.328 2.718 3.106 3.497 4.025 4.437

12 0.259 0.695 1.356 1.782 1.912 2.179 2.303 2.681 3.055 3.428 3.930 4.318

13 0.259 0.694 1.350 1.771 1.899 2.160 2.282 2.650 3.012 3.372 3.852 4.221

14 0.258 0.692 1.345 1.761 1.887 2.145 2.264 2.624 2.977 3.326 3.787 4.140

15 0.258 0.691 1.341 1.753 1.878 2.131 2.249 2.602 2.947 3.286 3.733 4.073

16 0.258 0.690 1.337 1.746 1.869 2.120 2.235 2.583 2.921 3.252 3.686 4.015

17 0.257 0.689 1.333 1.740 1.862 2.110 2.224 2.567 2.898 3.222 3.646 3.965

18 0.257 0.688 1.330 1.734 1.855 2.101 2.214 2.552 2.878 3.197 3.610 3.922

19 0.257 0.688 1.328 1.729 1.850 2.093 2.205 2.539 2.861 3.174 3.579 3.883

20 0.257 0.687 1.325 1.725 1.844 2.086 2.197 2.528 2.845 3.153 3.552 3.850

21 0.257 0.686 1.323 1.721 1.840 2.080 2.189 2.518 2.831 3.135 3.527 3.819

22 0.256 0.686 1.321 1.717 1.835 2.074 2.183 2.508 2.819 3.119 3.505 3.792

23 0.256 0.685 1.319 1.714 1.832 2.069 2.177 2.500 2.807 3.104 3.485 3.768

24 0.256 0.685 1.318 1.711 1.828 2.064 2.172 2.492 2.797 3.091 3.467 3.745

25 0.256 0.684 1.316 1.708 1.825 2.060 2.167 2.485 2.787 3.078 3.450 3.725

26 0.256 0.684 1.315 1.706 1.822 2.056 2.162 2.479 2.779 3.067 3.435 3.707

27 0.256 0.684 1.314 1.703 1.819 2.052 2.158 2.473 2.771 3.057 3.421 3.689

28 0.256 0.683 1.313 1.701 1.817 2.048 2.154 2.467 2.763 3.047 3.408 3.67429 0.256 0.683 1.311 1.699 1.814 2.045 2.150 2.462 2.756 3.038 3.396 3.660

30 0.256 0.683 1.310 1.697 1.812 2.042 2.147 2.457 2.750 3.030 3.385 3.646

31 0.256 0.682 1.309 1.696 1.810 2.040 2.144 2.453 2.744 3.022 3.375 3.633

32 0.255 0.682 1.309 1.694 1.808 2.037 2.141 2.449 2.738 3.015 3.365 3.622

33 0.255 0.682 1.308 1.692 1.806 2.035 2.138 2.445 2.733 3.008 3.356 3.611

34 0.255 0.682 1.307 1.691 1.805 2.032 2.136 2.441 2.728 3.002 3.348 3.601

35 0.255 0.682 1.306 1.690 1.803 2.030 2.133 2.438 2.724 2.996 3.340 3.591

36 0.255 0.681 1.306 1.688 1.802 2.028 2.131 2.434 2.719 2.990 3.333 3.582

37 0.255 0.681 1.305 1.687 1.800 2.026 2.129 2.431 2.715 2.985 3.326 3.574

38 0.255 0.681 1.304 1.686 1.799 2.024 2.127 2.429 2.712 2.980 3.319 3.566

39 0.255 0.681 1.304 1.685 1.798 2.023 2.125 2.426 2.708 2.976 3.313 3.558

40 0.255 0.681 1.303 1.684 1.796 2.021 2.123 2.423 2.704 2.971 3.307 3.55160 0.254 0.679 1.296 1.671 1.781 2.000 2.099 2.390 2.660 2.915 3.232 3.460

80 0.254 0.678 1.292 1.664 1.773 1.990 2.088 2.374 2.639 2.887 3.195 3.416

100 0 254 0 677 1 290 1 660 1 769 1 984 2 081 2 364 2 626 2 871 3 174 3 390

Column headings denote probabilities () above tabulated values.

TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS

design notes and statistical tables

Documents