Class 05. Using the NormalIntro to Descriptive Statistics

EMBS Section 3.1, 3.2. and first part of 3.3

What we learned last class

• To love the NORMAL distribution?– IT IS FLEXIBLE

• Parameter μ lets you center it anywhere.• Parameter σ lets you specify the width (variance,

uncertainty)– If X is highly variable, pick a large σ

– NORMDIST makes probability calculations easy.• No need for converting x to z in order to use the table in

the book. No need for NORMSINV[(x-μ)/σ].

– It approximates the binomial when n is big• Just set μ=n*p and σ = [n*p*(1-p)]^.5

EMBS Fig 6.4, p 249

You can’t change the 68/95/99 breakdown.

You can’t make it skewed.

It is a pdf (prob density function).

The height is probability density.

Areas under the curve are

probabilities

If X~N(μ,σ)And Y=a+b*X,

ThenY~N(a+b*μ,b*σ)

Temp(C)~N(10,10)

-20 -10 0 10 20 30 40

Temp(F)= 32 + (9/5) Temp(C)

-4 14 32 50 68 86 104

Temp(F)~N(50,18)

Case: Lorex Pharmaceuticals

• Lorex produces Linatol (liquid medicine for high blood pressure)– Sold in 10-ounce bottles.– 600*12 = 7,200 fill attempts per shift– Linatol costs them $0.40 per ounce to make.– Bottles filled to more than 10 ounces get sold for

$186 per case of 12.– Bottles under-filled get sold as seconds at a 20%

discount ($148.8 per case)

Case: Lorex Pharmaceuticals

• The Filling Machine has an adjustable target. Test have shown that the fill amounts will be independent (across fill attempts) and– Normally distributed– μ = target– σ = 0.16 fluid ounces

• In other words (symbols?)– X ~ N(target,0.16)

What target should they use?

Worksheets….

Lorex Worksheet Minimum required 10

$186 $148.80

Target P(underfilled bottle)Expected Good

CasesExpected Bad

Cases Total CasesExpected Revenue

10.0 600

10.1 600

10.2 600

10.3 600

Fill Test DataNormal(10.2,0.16)?

EXHIBIT 2LOREX PHARMACEUTICALS

Filling Line Test Results with Target = 10.2

9.89 10.41 10.53 10.20 10.23 10.1510.17 10.17 10.32 10.04 10.48 10.1110.29 10.35 10.16 10.16 10.17 10.1910.00 10.06 10.21 10.22 9.76 10.2210.04 10.19 10.09 10.12 10.06 10.1010.35 10.17 10.02 10.36 10.17 9.9910.05 10.07 10.32 10.24 10.04 10.4010.19 10.27 10.14 10.07 10.41 10.7610.21 10.13 10.11 10.40 10.27 10.209.79 10.24 10.20 10.29 10.00 10.31

10.53 10.14 10.35 10.21 10.23 10.1610.47 9.84 9.96 10.10 10.11 10.2310.24 10.36 10.30 10.23 10.19 10.1710.17 10.11 10.33 10.19 9.97 10.0010.15 10.42 10.36 10.19 10.05 10.1110.06 10.16 10.17 10.29 10.12 10.3010.13 10.21 10.15 10.25 10.33 10.6410.04 10.01 10.14 10.18 10.18 10.1010.20 10.25 10.07 10.42 10.54 10.2310.37 10.44 10.37 9.85 9.91 10.4510.24 10.44 10.40 10.45 10.28 10.1710.03 10.44 10.25 10.37 10.23 10.1910.01 10.13 10.24 10.22 9.98 9.9810.20 10.29 10.03 10.19 9.99 10.13

Fill Test DataDescriptive StatisticsSummary Statistics

Amount

Mean 10.198Standard Error 0.014Median 10.190Mode #N/AStandard Deviation 0.163Sample Variance 0.026Kurtosis 0.771Skewness 0.245Range 0.997Minimum 9.758Maximum 10.756Sum 1468.542Count 144

Fill Test DataHistogram

Bin Frequency9.758 19.841 29.925 3

10.008 1010.091 1710.174 3310.257 3610.340 1410.423 1610.506 710.590 310.673 1More 1

9.7589.841

9.925

10.008

10.091

10.174

10.257

10.340

10.423

10.506

10.590

10.673More

0

5

10

15

20

25

30

35

40

Histogram

Frequency

Bin

Freq

uency

Assignment for class 06

• Find some numerical data• Get it into excel in one column with a label at the top• Data Analysis (File, Options, Addins, Go, check analysis

ToolPak, okay)– Descriptive Statistics

• Check “summary statistics”

• One sheet– A brief description of the data and where you got it.– A printout (or hand copy) of the summary statistics– A brief answer to the question…could these data have come

from a normal distribution…why or why not?

Completed and extended worksheet

Lorex Worksheet Minimum 10

$186 $148.80

Target P(underfilled bottle)Expected Good

CasesExpected Bad

Cases Total CasesExpected Revenue

Expected Cost

Expected Contribution

10.0 0.5 300.00 300.00 600 $100,440 $28,800 $71,640

10.1 0.266 440.41 159.59 600 $105,663 $29,088 $76,575

10.2 0.106 536.61 63.39 600 $109,242 $29,376 $79,866

10.3 0.030 581.76 18.24 600 $110,922 $29,664 $81,258

10.4 0.006 596.27 3.73 600 $111,461 $29,952 $81,509

10.5 0.001 599.47 0.53 600 $111,580 $30,240 $81,340

10.6 0.000 599.95 0.05 600 $111,598 $30,528 $81,070