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Exam 1 Fall02

Last year the proportion of female applicants who received financial aid was greater than the proportion of

male applicants who received financial aid. The graduate student council decides to determine if this

situation has been true for the past five years. A simple random sample of 1569 students was selected from

a list of all financial aid applicants (male and female during the past five years. The results are shown onthe following table.

!ale "emale Total#eceived financial aid $%9 5&9 1'1%

id not received financial aid )5$ 19* 551

Total %$) *&6 1569

Answer +uestions 1 to 5 using this information.

1. ,hich of the following is the proportion of male applicants in the past five years-(a '.)51&

(b '.$6&*

(c '.5)*)

(d '.6$%%(e '.*'&1

&. ,hich of the following is the proportion of all applicants who did not receive financial aid during the

past five years-(a '.)51&

(b '.$6&*

(c '.5)*)

(d '.6$%%(e '.*'&1

). ,hich of the following is the proportion of all applicants who are male and received financial aid

during the past five years-(a '.''*5

(b '.1&56

(c '.&&56

(d '.)11*(e '.))*&

$. ,hich of the following is the proportion of male applicants who received financial aid during the past

five years-(a '.$%'$

(b '.519*

(c '.5%'1(d '.6&))

(e '.*&%*

5. o the data collected during the past five years confirm the proportion of female applicants whoreceived financial aid being greater than the proportion of male applicants who received financial aid-

(a es(b /o

6. 0n a sample of n1'' observations2 the density and the relative fre+uency for the class interval are '.'1

and '.1$ respectively. ,hich of the following is the width for the same interval-

(a '.'1

(b '.1$(c 1

(d 1$

(e 1''

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Exam 1 Fall02

According to a recent study2 the number of people susceptible to a restaurant syndrome2 a reaction lin3ed to

the food seasoner has been e4aggerated. A particular researcher reported that in a study of diners2 only 5

percent reported sensations commonly associated with the syndrome. 0f four unrelated people dine in a

particular restaurant chosen2 answer the following ) +uestions using this information.

*. ,hat is the probability that all four will e4perience the syndrome-

(a '.''''

(b '.'1)5(c '.1%55

(d '.%1$5

(e '.9999

%. ,hat is the probability that e4actly two of the four will e4perience the syndrome-

(a '.''''

(b '.'1)5

(c '.1%55(d '.%1$5

(e '.9999

9. ,hat is the probability that at least one of the four will e4perience the syndrome-

(a '.''''(b '.'1)5

(c '.1%55

(d '.%1$5(e '.9999

An e4periment generates a sample space containing eight simple outcomes 12 &22%with 7(i18%2

i12&2)22%. The events A and are defined as A:12$26; and :)2$25262*;. Answer +uestions1' to 1$ using this information. (enn diagrams are ?@.

1'. ,hich of the following is the probability of A2 7(A-

(a &8%

(b )8%(c 58%

(d 68%(e *8%

11. ,hich of the following is the 7(A-

(a &8%

(b )8%(c 58%

(d 68%

(e *8%

1&. ,hich of the following is the 7(A-

(a '.&&

(b '.$'

(c '.5*(d '.6*

(e '.%&

1). Are events A and mutually e4clusive-

(a es2 7(A'

(b es2 7(A7(A7(

(c /o2 7(A'

(d /o2 7(A7(A7(

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Exam 1 Fall02

(e /o2 7(A7(A

1$. Are events A and independent-

(a es2 7(A'

(b es2 7(A7(A7(

(c /o2 7(A'

(d /o2 7(A7(A7(

(e /o2 7(A7(A

?bservations on burst strength (lb8in& were obtained both for test noBBle closure welds and for production

canister noBBle welds. The results are shown on the following table

Test 5&'' *&'' 61'' *)'' *)'' %''' *$'' *)'' *)'' %''' 6*'' %)''

Canister 5&5' 56&5 59'' 59'' 5*'' 6'5' 5%'' 6''' 5%*5 61'' 5%5' 66''

The following comparative bo4plots and the descriptive statistics are obtained using !0/0TA software.Variable N Mean Median StDev Minimum Maximum Q1 Q3

Test 12 7175 7300 854 5200 8300 6825 7850

anister 12 5887!5 5887!5 317!" 5250 6600 5725 6037!5

Test Canister

5000

6000

7000

8000

Answer +uestions 15 to &) using the information above.

15. ,hich is the s3ewness of the canister data-

(a 7ositively s3ewed(b /egatively s3ewed

(c Dymmetric

(d /one of the above

(e All of the above

16. Are there any outliers for canister data-

(a /o outliers

(b 1 outlier(c & outliers

(d ) outliers

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Exam 1 Fall02

(e $ or more outliers

1*. ,hat proportion of the strength are at least 59'' for the canister data-

(a '.&$(b '.))

(c '.5'

(d '.6*

(e '.*6

1%. ,hat proportion of the strength are between its mean and the median for the canister data- (e4clusive

(a '

(b '.'%)(c '.5$9

(d '.91*

(e 1

19. ,hat is the *5thpercentile of the strength for the test data-

(a 5*&5

(b 6')*.5

(c 6%&5

(d *)''(e *%5'

&'.

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0f the components 1 to ) wor3 with probability '.9 and the components $ to 6 wor3 with probability '.% on

the following mi4ed system2 answer +uestions &$ and &5 using this information.

FFFFFFFFFFF& FFFFFFFFF)FFFFFFFFFFF 8 G

FFFFFFFFF 1 FFFFFFFF8 GFFFFFFF 6 FFFFFFFF

G 8

GFFFFFFFFFFF$FFFFFF FFF 5 FFFFFFFFFF 8

&$. ,hich of the following is the probability for the system to wor3-

(a '.&%')

(b '.)&9&(c '.6*'%

(d '.*19*

(e '.%&$5

&5. 0f all 6 components were connected parallel instead of the given mi4ed system2 would the probability

for the system to wor3 higher-

(a es

(b /o

Answer Key:1! 2!# 3!D 4! 5!# 6!D 7!# 8!$ "! 10!$ 11!D 12!$

13! 14!D 15! 16! 17! 18!# 1"!% 20! 21! 22! 23! 24!

25!#

Some of the formulas that you may need

Relative Frequency "re+uency 8 sample siBe. ensity #elative "re+uency 8 class width!he Ran"e:# the largest data E the smallest data !he #nterquartile ran"e:0H# H) E H1

$oefficient of variation: C>1''(F

8 xs $oefficient of S%ewness: D@s

medianx ()F

!he sam&le mean of '(s= =

=1

F

8i

i nxx . !he sam&le variance of '(s=

1

(&F&

&

=

n

xnx

s i

i

!he sam&le standard deviation of '(s= &ss =

)utually exclusive or is*oint: Two events2 A and have no outcomes in common.

$onditional +ro,a,ility: "or any two events A and with 7(I'2 the conditional probability of A given

has occurred is defined by 7(A 7(A 8 7(.

#nde&endence: Two events A and are independent if 7(A 7(A7(

"or any two events A and 2 7(A 7(A J 7( E 7(A.

"or any three events2 7(AC7(A J 7( J 7(C E 7(A E 7(ACE 7(C J7(AC.

"or any three events2 7(A7(ACJ 7(ACK.

+redictin" the Relia,ility of Systems with n com&onents:

#i(t= The reliability of individual component 7(component i survives beyond time t

#s(t= The reliability of the system 7(system wor3s

Deries Dystem #s(t#1(t#&(t.#n(t

7arallel Dystem #s(t 1 E 1E#1(tM1E#&(tM1E#n(tM