Exercises For Chapter 6

MULTIPLE CHOICE. Choose the one altemative that best completes the statement or answers the question.

/1 Suppose that all the values in a data set are converted to z-scores. Which of the statements below is 1) _ true?

1: The mean of the z-scores will be zero, and the standard deviation of the z-scores will be the same as the standard deviation of the original data values. 2: The mean and standard deviation of the z-scores will be the same as the mean and standard deviation of the original data values. 3: The mean of the z-scores will be 0, and the standard deviation of the z-scores will be 1. 4: The mean and the s~ard deviation of the z-scores will both be zero.

A) 2 &3 C) 4 D) 1 E) Both A&B

;'2{Find the area of the indicated region under the standard normal curve.

, ~~L'i; < _\.'3>} '"

-1.30 0

A) 0.4032 B) 0.5968 ~.0968 D) 0.0823 E) 0.9032 \

3{ Find the area of the indicated region under the standard normal curve. 3) _

" ~_\.\~) +~lt 7';;t-D'3.}

-1.13 0 2.03

A) 0.8489 B) 0.0212 @:l.1504 D) 0.1714 E) 0.1292

ind the z-scores for which 98% of the distribution's area lies between -z and z. 4) _

~.(-1.645, 1.645) ~ f"") ".'j ... '\ ,,<'\ b'-J(-2.33, 2.33) ~l ,~ ~: :r <: '-4 e; e ~) -;. (-0:99,0.99) . ~~'1 -"2.

D) (-2.06,2.06) ..,\E) (-1.96, 1.96) ... \ ." ........

(;. '2 ssume that the salaries of elementary school teachers are normally distributed with a mean of 5) _

$32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that he or she makes less than $28,000. ~

A) 0.9981 .. B) 0.4082 . 0.0918 D) 0.9827. E) 0.2113

6) _~ss~m~ :~:ii::l~il of~!~a~ SC~~1:;~~~s)re~~;Ja1l;di:~~~~~~ith a mean of $34,000 and a standard deviation of $2000. What is the maximum salary for teachers in the bottom 10%? - ­

A) $34,330 B) $36,560 C) $30,710 ~31,440 E) $37,290

.p( ~ ~ XIo) )

z.; -,1

,is<~Q):: .~\\?

~ l 'j.,. ~)C,,) \ :: "~ ~ IIIiil!I' ~ '&i. • 1#.. ~<:._:._~~),: --:~l.· . . SCi'g1 4t •Go2k .. eeln .,~~~

bank's loan officer rates applicants for credit. The ratings are normally distributed with a melfn of 7) _ 200 and a standard deviation of 50. F~~.the sixtif:~:£rrcentile, i.e., P60,(the score which separates

the lower 60% from the top 40%). A) 211.3 B) 207.8 C) 2.2:1.5 ~12.5 E) 187.5

'i.. \J =. 2.' (sC) ~c.; ~ , e weekly salaries of teachers are normally distributed with a mean of $490 and a standard 8) _

deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

A) 0.7823 @.2177 C) 0.1277 D) 0.4354 E) 0.2823

pC", ~S '2 S. ) :- 1){ 1: , "1~) -:: ~ S - ,'( 8'2 :.2\" 9) _A If we know that the length o(fune it takes a college student to find a parking spot in the library

parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. ~

A) 0.3551 B) 0,:':15 C) 0.8085 ~0.3085 E) 0.2674

'f(~<?» ~ fl2 < -OIS) ;::= o3t>~S f we khow that the length of time it takes a college student to find a parking spot in the library 10) _

parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5

mi~~~:nd a par~;;~ the librarybar:.~ot. 0) 0.4938 E) 0.0919 • g<l ,.., -=--:-~ \'( 2 <~,< 4,~) ~. \~l--\\s <' I' :'..\.(j32 +-·1,~t3 ;:)

The time needed to complete' a final examination is normally distrtbuted with a mean of 80 mintes and a standard deviation of ten minutes. What is the probability of completing the exam in one hour or less?

A) .4772 B) .5228 C) .5 \ D) .9772 (!Do228

?( '1... ~ "0) ~ ? -2 1~ -s - ,'-\'112 ~ , The time needed to complete afinal examination is normally distributed with a mean of 80 mintes 12) _

and a standard deviation of ten minutes. Assuming that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allowed time?

A) about 5 students 0 I -..J.... ..... C\ t..) '\. ':'..••.,about 10 students , \.. ]....' ,-, ~(t2~ -, \ ) about 15 students I")

D) about 8 students W"::;;' "::> - \S'-'\ \ ~ z: \ \S'&~1 E) about 50 students

.: .. i-...=, ,~::.31 ~(OO

Given that Z is a standard normal variable, the value ZI for which P(Z s ZI) == 0.242 is: 13) _

A) -0.65. 0])0.70. ...". C) 0.70. D) -.O~~"i,..~c,~., :~O.65.

~

The owner of a fish market t~rm~~dt~ l ~a~~g; ~~'~tfor a c~tf~:~}b~~d~:ith a 14) _

standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above '\ weight (in pounds) do 89.80% of the weights occur?

A] .184 pounds ' .

) 2.418 pounds p . ",\ .. ~ C\ ~\ C) 4.216 pounds L'" '/ f\ 0 J z: D) ~.27 pounds

E) 2.992 pounds ? l 7:- '7 ?-o )

~ i)';:' 2

I

15) _ ~ A continuous random variable may assume: Aonlyfractional values Wall values in an interval.

C) onlyinteger values D) all of the above. E) none of the above

Fahd has a pizza business. The times to prepare and deliver pizzas are approximately normally 16) _ distributed with mean 18 minutes and standard deviation 9 minutes. Fahd advertises "If it takes more than 30 minutes to get your pizza, you get it free". Approximately, what percent of pizzas does Fahdhave to give~ay free? (choose the answer to th'e nearest integer) ..

A) 41% 0,;9% C) 4% D) 16% E) 46%

, \) \. ~"7 ~ b J := 'V (?- ""7 \ \11 \ -:::. s- '\ '--\ ()~ 1- ~ I o q The average time it takes for a letter to reach from one place to another is 3.2 days, with a standard 17) _ deviation of 0.85 days. What is the prob~'pility that a letter arrives at its destination wjthin tWo . days after mailing? (i.e. in four days orless) Y'- 'J... ~ '-\.') .::? t"2: < ,~'V\'\ := •5 +:~2b\J , A) .0.1736, ~.8264 C) 0.6528 D) 0.6736 E) 0.3264

\

~ Phone calls for an Insurance company were put on hold for extended periods of time. Suppose that 18) _ the waiting time on hold followed a normal distribution with mean 12 minutes and standard deviation 4 minutes. Find the probability that a randomly selected caller waited less than 17.6

minutes on hold. \? \.. "'f..-. < \'1' b ) -:: p l Z- < \"'-\)' ~

G) ?9192 ~) 0.5808 C) 0.4192 D) 0.0808 E) 0.4222

)'l>Phone calls for an Insurance company were put on hold for extended periods of time. Suppose that 19) _ the waiting time on hold followed a normal distribution with mean 12 minutes and standard deviation 4 minutes. What proportion of the callers had to wait between 6 and 10 minutes on hold?

00.2417 B) 0.4332 C) 0.2583 D) 0.6247 E) 0.1915

.P l 6 ~"" <. \l.J) ~ Pl-\'S< t<~ ,5; ) x: Phone calls for an Insurance company were put on hold for extended periods of time. Suppose that 20) _ the waiting time .on hold followed a normaldistribution with mean 12 minutes and standard deviation 4 minutes. Tile compan~~es. to offer letters of apology to the 4% ofthe callers Who waited on ho'Jd longest. How long did thes~fthe callers have to wait on hold?

A) At least 18 minutes . . '\ ~ B) At least 23 minutes ~l '/... ii.Q )~, 0\1 ~

.R At least 22 minutes '11 / "" c)

(E)lAtleast 19 minutes ~C 'C ~ 7;:-;;:,) :; \ 0 ~_. .~ E) At least'Zt] minutes ~c -;:. '-I b .~ ~-:. \-I b( l.\l + 11 ,~b

-::: \c\,u\.\. e hundr students took a test on which the mean score was 73 with a variance of 64. A grade 21)r -- ­

"A was given to all who scored 85 or more. Approximately, how many A's were there, assuming scores were normally distributed?(Choose the closest)

A) 42 . (!}>7 . C) 43 D) 58 E) 5 1v -..:J

C~)'~<;) -:; 1><..9;-/\'<;') =- ·S- .. \'\'3>]2. ~·.,obb~ *1'\ ~ ", 6<g ~1-arks on a math test o~ 600 students follow a normal distribution with a mean of 65 and a standard 22) _

deviation of 12. The number of students scoring between 56 and 74 is

A) 272 (!) 328 C) 260 D) 164 E) 180

P(S6 C ~ <1"\ ) 3

-z: Pl-flS <:..~ c "15)0

z: 2. (:2-, 3\1\ )

~ "S~ I/b y. Goo

.I.l

The scores on a university examination are normally distributed with a mean of 62 and a standard 23) __ deviation of 11. If the bottom 5% of students will fail the course, what is the lowestmark that a student can ";;ve and still be awarded passing grade? (chose the closest) ­

~o-,..A) 41 B) 42 C) 54 D) 50 ~44

'\:>( 'b. ..< :i9 ') :=. 05 ~ ~c...., ,bS "Ao '-\.\3, ~s r-:. ~'1'::'6\ I) The distfibution of final exam scores in a statistics class is a normal with a standard deviation 60. If 24) _

)~ 93.32% of the students received scores no higher than 250, then the mean score is: "2.-s-<J- u... A) 200 0160 C)150 D) 60 E) 90 (,S=. b;;

'l"'" ~ fJ-&-0 ') :::. C\,3.?, '2 -4'> \'l'C ~'2 u) -:: ,C\3 ~ 2-~ 'J:-", ........ \.~ M" ~ In a normal distribution with mean 30 and ~nce 25, what percent of scores fall below 42? 25) /

A) 5Q.82% B) 49.18% ,~9.18% D) 88.9% ~) 0.82%

\' l "J.. <\.\ 2) -z: ~ l r < :l,'-t ") -::: •C\ ~ \g~ "J... \0 0

~The time required to assemble an e\ectronic component is normally distributed with a mean of 12 26) _

minutes and a standard deviation of 1.5 minutes. Find the probability that a particular assembly takes more than 14.25 minutes.

A) 0.5668 ® 0.0668. C) 0.4332 D) 0.9332 E) 0.4421

P\. 'I-.. ') \\.\ /2 ~\ -:: Pl '"2: ') '\ •5) .z: The height of an adult·nIl.ale is known to be normally distributed with mean of 175 cm and standard 27) _

deviation 6 ern. The 20th per~ of the d~ibution of heights is: ~ln ~1~ ~lro ~ln ~1~

p~ ;::" C~ <. ~0)) -:.,L. #S) The cost of treatment per patient is modeled by an insurance company as a normal random 28) _

, variable with mean $775 and standard deviation $150. What is the probability that the treatment cost of a patient is less~n $1000?

A) 0.6826 ~0.9332 C) 0.8531 D) 0.4332 E) .5668

P \. 'I-. < \000) z: ~ ( C < \.s )/9) Assuming that the monthly food expenditures of families of a certain size in one economic group 29) _

are approximately normally distributed with a mean of $130 and a standard deviation of $20. What proportion of the expenditures are les~,an $90? .

A) .9732 B) .97n <:S:2fi228 D) .47n E) .5228 •

l Pc. "" -< C\ 0 \ ~ \> (-t:- <-2 ")-=}O) Assuming that the mohthlY food expenditures of families of a certain size in one economic group 30) _

are approximately normally distributed with a mean of $1~0 and a standard deviation of $20. What percentage of the expenditures are between $100 and $120? .

A) .1915 . ®i2417 C) .6915. . D) .9332 E) .4332

\' L \oo « X <\20"\ -z: p (- \"S' < Z. C- - ~S, Assuming that the m'onthly food expenditures of families of a certain J,ze in one economic group 31) _

are approximately normally distributed with a mean of $130 and a standard deviation of $20. What percentage of the expenditures are either less than $120 or more than $150?

A) .5643 " B) .1498 C) .1587 D) .3085 ~672 , ,

? \.i-. -< Qo') "\-? l "'k -; \ ~ ') ~ Vl C· <- 'S") T o ( ?:: j \) _ ,1~BS ""'" (t , ,3\\\3. Assuming that the monthly food expenditures of families of a certain si~e in one economiC-group I 32) , are approximately normally distributed with a mean of $130 ,"?d a st~ndard deviation of $20. •'\

Above what value does the top 14 percent, of the expenditures he? P l t; '7 X"1 x: .. \ \\ ~." A) 162.3' @151.6 . C) 108.4 _ D) 156.1 E) 168.1 ... ~.-;~

\> t rc-7 ?'-~J.-;. ,\ \.\ ,r 0

) The scores on a Statistics test follow a normal distribution with a mean of 65 and a standard 33) . \·tli deviation of 12. Approximately, what perce e of students have scores below50?_ -.---­

A) 11.25% B) 39.62% C 0.38% D) 40.12%~ E) 60.38% C?!.C\l\ .1~. '3~

P ( "i <, So J · ~~1 'f.,~o \~~'l.i». '\ \405 b ~ Ie> ,5 0."? (~ <- \,'2-5) - • ~

------

>t"~ \?q~ e ply;.. < ~Q ~ ~,~ ~ ~~ ':. \"l~ . ' .. f II Id' tributi ith )\;.,~f6-5·.. "R.l'~·)dt'~ __The scores on a 5tatistics test 0 ow a norma 1S 1 ution W1 a mean 0 ana r"slanaa:r . 34)

deviation of 12. What is the approximate 90th percentile of the mark (score) distribution? A) 30.36 B) 85.90 C) 82.65 D) 83.25 ~0.36

The distribution of weights of a large group of is normally distributed with a mean of 80 kg. 35) _ Approximately 68.26% of the weights are between 70 and 90 kg. What is the value of the standard deviation of the distribution of weights? (910 B) 5 C) 3 D) 15 E) 2.5

~According to a study, men devote an average of 16 hours per week to housework. Assume that the 36) _ number of hours men devote per week to housework is normally distributed with a mean of 16 hours and a standard deviation of 3.5 hours. Find the probability that a randomly selected man spends between 12 anc;R hours per week to housework

. A) .8729 ~.8293 C) .4564 D) .9564 E) .3729

P \ \L < 'X.. <2..~) z: 1> (-\ ,\~ <.:2.: < \:'\\ \ -z: ~ According to a study, men devote an average of 16 hours per week to Housework. Assume that the 37) _

number of hours men devote per week to housework is normally distributed with a mean of 16 hours and a standard deviation of 3.5 hours. What is the probability that a randomly selected man spends more than 20 hours per week to housework? ~.127~ B) .2379 C) .6276 D) .3729 E) .8729

~l 'j., 7'Lo ') rz: p\" ~ ~ \' \,-\ \ :::: · \'L 1 \ According to a study, men devote an average of 16 hours per week to housework. Assume that the 38) _ number of hours men devote per week to housework is normally distributed with a mean of 16 hours and a standard deviation of 3.5 hours. Suppose that the 10% of men ""ho.~p.~!1-<ltb.eJ.e_asttime

\ "." . ..~' ~_""'_~"''''"'·''S~''''·~_''''''''' ., , .......... ~useworkde~e fewer than x hours per week to nousework. Find x, .

l)fJ 11.52 B) 15.12 C) 20.48 D) 12.52 E) 11.25 ,'/\ "

Pl ~"'" y.". \j ) -;. • \ ~ /::3 <S-P; <.y\ 0 ~ 0J jJ\ J \f! \ ~ • '" .~ b'1?C? '") ")r

<;y 7"l i oJ l- 'f.. cY <.Y \ tJ~ ~ '~-_.--;.:. , ':;) 1.\ ,..) e: " ~A u ~')JJ l.

, / \ t-~~ \ \ ~':' ~g~"-_.... '«;

t:::"-:.\o

\ __ b("61 C~

": \ '1 \i~

5

Answer Key Testname: EXERCISES FOR CHAPTER 6

1) B

2) C 3) C

4) B

5) C 6) D 7) D 8) B

9) D 10) B 11) E

12) B

13) B

14) A 15) B 16) B

17) B

18) A

19) A

20)D 21) B

22) B 23) E

24) B 25) C 26) B

27) C 28) B 29) C

30) B

31) E

32) B

33) C

34) E 35) A

36) B 37) A

38) A

6

Exercises For Chapter 6

MULllPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

;nSuppose that all the values in a data set are converted to z-scores, Whichof thestatements below is 1) _ true?

1: The mean of thez-scores will be zero, and the standard deviation of the z-scores will be the same as the standard deviation of the original data values. 2: The mean and standard deviation of the z-seores will be the same as themean and standard deviation of the original data values. 3: The mean of thez-scores will be 0, and the standard deviation of the z-scores will be 1. 4: The mean and the ~dard deviation of the z-scores will both be zero.

A) 2 &3 q 4 0) 1

J Find the area of the indicated region under thestandard normal curve.

flt: < - \.3» ~

-1.30 0

A) 0.4032 B)0.5968 . ~)'0968 0)0.0823

j \

Find the area of the indicated region under ~ standard normal curve.

~_\.\3) +~l-:Z:

-1.13 0 2.03

A) 0.8489 B) 0.0212 @xl.1504 D) 0.1714

E)BothA&:B

2) _

E) 0.9032

3) _

E) 0.1292

ind the z-scores for which 98% of the distribution's area lies between -z and z.

~ (-1 . 645' 1.645)

1 -2.33,2.33) (-0.99,0.99)

D) (-2.06, 2.06) E) (-1.96,1.96)

4) _

sume that the salaries of elementary school teachers are normally distributed with a mean of $32,000 and a standard deviation of $3000.If a teacher is selected at random, find theprobability that he or she makes less than $28,000. ~

A) 0.9981 B) 0.4082 \Q.;'.0918 D) 0.9827 E) 0.2113

5) _

Assume that the salaries of elementary school teachers are normally distributed with a mean of $34,000 and a standard deviation of $2000.What is the maximum salary for teachers in the bottom 10%?

A) $34,330 B) $36,560 C) $30,710 ®31,440 E) $37,290

6) _

1

• bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 7) 200 and a standard deviation of 50.Find the sixtieth percentile, i.e., P6Q,(the score which separates

the lower 60% from the top 40%). A) 211.3 B) 207.8 q221.5 (9)12.5 E) 187.5

I

"'The weekly salaries of teachers are normally distn'buted with a mean of $490 and a standard 8) Wdeviation of $45.What is the probability that a randomly selected teacher earns more than $525 a

week? A) 0.7823 @>.2177 q 0.1277 D) 0.4354 E) 0.2823

A Ifwe know that the length of time it takes a college student to find a parking spot in the library 9) parking lot follows a normal distn'butibn With a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. ~

A) 0.3551 B) 0.1915' q 0.8085 ~v.3085 E) 0.2674

. f t ~ < 3» z f l ~ < - 0 ,S) ==. 3 c 3 S 10 If we know that the length of time it talCes a college student to find a parking spot in·the library 10)@

parking lot follows a normal distribution with a mean of 3.5minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a par~t in the library parking lot.

A) 0.2255 ~.7745 q 0.0668 D) 0.4938 E) 0.0919

I;i\.The time needed to complete a final examination is normally distributed with a mean of 80 mintes 11)V and a standard deviation of ten minutes. What is the probability of completing the exam in one

hour or less? A) .4772 B) .5228 q .5 D) .9772 (])o228

e:The time needed to complete a final examination is normally distributed with a mean of 80 mintes 12) . and a standard deviation of ten minutes. Assuming that the class has 60 students and that the

examination period is 90 minutes in length. How many students do youexpect will be unable to complete the exam in the allowed time?

A) about 5 studentsfBi about 10 students "'d about 15 students

D) about 8 students E) about 50 students

, Given that 2 is a standar~ normal variable, the value 21 for which P(Z S 21) = 0.242 is: 13)

A) -0.65. ®0.70. C) 0.70. D) -.072 E) 0.65.

I I

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a 14) standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above

eight (in pounds) do 89.80%of the weights occur? .184 pounds~ 2.418 pounds

q 4.216pounds D) 1.27 pounds E) 2.992pounds

2

_

_

_

_

_

_

_

_

;I> A continuous random variable may assume: 15) _ ~only fractional values Wall values in an interval. q only integer.values D) all of the above. E) none of the above

eFahdhasa pizza business. The times to prepare and deliver pizzas are approximately normally 16) _ distributed with mean 18 minutes and standard deviation 9 minutes. Fahd advertises ''If it takes more than 30 minutes to get your pizza, you get it free". Approximately, what percent of pizzas does Fahd have to give~y free?(choose the answer to thenearest integer)

A) 41% clr% q 4% D) 16% E) 46% ,

€ )The average time it takes for a l~ to reach from one place to another is 3.2 days, with a standard 17) _ deviation of 0.85days. What is the prob~ty that a letterarrives aUts destination within four days after mai.Jini? (i.e.in four days or less) , .

A) ,0.1736 r-- ~.8264 q 0.6528 . D) 0.6736 E) 0.3264 \ . .

J) Phone callsfor an Insurance company were put on hold for exten~ periods of time. Suppose that 18) _ the waiting time on hold followed a normal distribution with mean 12 minutes and standard deviation 4 minutes. Find the probability that a randomly selected aner waited less than 17.6

minutes on hold. '? \.~ < ,." br -:: p l ~ < \..."\) ::: G) ?9192 ~) 0.5808 q 0.4192 D) 0.0808 E) 0.4222

)'IfPhone calls for an Insurance company were put on hold for extended periods of time. Suppose that 19) _ the waiting time on hold followed a normal distribution with mean 12 minutes and standard deviation 4 minutes. Whatproportion of the callers hadto wait between 6 and 10 minutes on hold?

00.2417 B) 0.4332 q 0.2583 D) 0.6247 E) 0.1915

"'. ~p C··b· <.1.. -< \\:>} ';:" Pl-\'S.<: c<~,s. \ :::ePhone callsfor an Insurance company were put on hold for extended pericx1s of time. Suppose that 20) _ the waiting time on hold followed a normal distribution with mean 12 minutes and standard . deviation 4 minutes. Thecompany wishes to offer lettersof apology to the 4% ofthe callers Who waited on hold longest.Howlongdidthese4% of the callers haveto wait on hold?

A) At least 18 minutes B) At least 23 minutes

.RAt least 22 minutes (EJAt least 19 minutes

E) At leastl20 minutes

~e hundred students took a test on which the mean score was 73 with a variance of 64. A grade 21) _ ~~~. was given to all who scored 85 or more. Approximately, how many A's were there, assuming

scores were normally distributed? (Choose the closest) A)42 ".~7 C)43 D) 58 E)5

~arkson a math test of 600 students follow a normal distribution with a mean of 65 and a standard 22) _

deviation of 12. The number of students scoring between 56 and 74 is

~m ~m C)~ ~W ~W

3

• The scores on a university examination are normally distributed with a mean of 62 and.a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded passing grade? (chose the closest) ~~ m~ qM ~~ ~«

• The distribution of final ex~ scores in a ~tistics class is a normal with a ~~d deviation 60.If 93.32% of the studentsJ&.ce1ved scores no higher than 250,then the mean store IS:

~~ ~~ q~ ~6O ~~

~ In a normal distribution with mean 30and ~ce25, what percent of scores fall below ~? A) 5Q.82% B) 49.18% . ~.18% 0) 88.9% ~ 0.82%

?l'J.. <\.\2..) ';::' ~l r -< ~ ..\.\ '. -;: .qq \& ~~\C)a )lffThe time requirl!d to assemble an e\ectronic component is normally distributed with a mean of 12

minutes and a standard deviation of 1.5 minutes. Find the probability that a particular assembly takes more than 14.25 minutes.

A) 0.5668 ®0.0668 q 0.4332' D) 0.9332 E) 0.~1

P\.~ '> \\.\ /2 S\ ~ \' lc ')" S) .:: • Theheight of an adultnW.e is known to be normally distributed with mean of 175 em and standard

deviation 6 em. The 20th percentile of the ~bution of heights is: ~m ~m ~m ~m ~~

j) The cost of treatment per patient is modeled by an insurance company as a normal random variable with mean $775 and standard deviation $150. What is the probability that the treatment cost of a patient is less~ $10007 "

A) 0.6826 ~0.9332 C) 0.8531 D) 0.4332 E) .5668

P l ~ <\0(0) ::: ~ ( 2: < \ ,S ) ~ Assuming that the monthly food expenditures of families of a certain size in one economic group

are approximately normally distributed with a mean of $130 and a standard deviation of $20. What proportion of the expenditures are les~$907 . ,

~~ ~~ ~ ~~ m~

Pl. "" -< q 0"\ ~ ,,(7= <-"2. "')-=)0> Assuming that the mohthly food expenditures of families of a certain size in one economic group are approximately normally distributed with a mean of $130 and a standard deviation of $20.

What percentage ofth~ndituresare between $100 and'$120? . A) .1915 ~2417 C) .6915. . D) .9332 E) .4332

" L\p'o c OX- <\ 2<::;\ ':=' 'P c, v.s <, c <- ~S\~!AsSUming that the m'onthly food expenditures of families of a certain Jze in one economic group

are approximately normally distributed with a mean of $130 and a standard deviation of $20. What percen~ageof the expenditures are either less than $120 or more than $150? ~A

A) .5643 B) .1498 q .1587 D) .3085 ~672 '. . .

• Assuming that the monthly food expenditures of families of a certain size in one economic group are approximately normally distributed with a mean of $130 and a standard deviation of $20. Above what value does the top 14 percent of the expenditures lie?

A) 162.3 @151.6-, C) 108.4 D) 156.1 E) 168.1

~ The scores on a Statistics test follow a normal distribution with a mean of 65 and a standard /'"" deviation of 12. Approximately, what per e of students have scores below 507

A) 11.25% B) 39.62% C 0.38% D) 40.12% E) 60.38% , A

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• The scores ~ a Statisticstest follow a normal_~~~~~~~~~~~~..~f. ~~~!l ~~~. .... ..34).--.....= -·--deviatiorrof 12~ Wbat1Sllie approXiiilafi9lJfl\ percentile of the mark (score) distrIbution?

A) 30.36 B)85.90 q 82.65 D) 83.25 (!!PJ.36 !aJ.-. _The distribution of weights of a large group of is normally distributed with a mean of 80 kg. 35) __ -I' Approximately 68.26% of the weights are between 70and 90kg.What is the value of the standard

deviation of the distribution of weights? ,/ (910 B) 5 q 3 D) 15 E) 2.5

;4According to a study, men d~ote an,average of 16hours perweek to housework.Assume that the 36) _ number of hours men devote perweek to housework is normally distributed. with a mean of 16 hours and a standard deviationof3.5hours. Find.the probability that a randomlyselected man spends '6etween12antiit hours perweek to housework

A) .8729 . _~8293 q .4564 D) .9564 E) 3729

P l\'l..< )«2.2...\ . = ~\.-\.\,,\ <:e<.\:'\\ '\ :::jffl'According to a study, ~ devote an average of 16hours perweek to Housework. Assume that the 37) _

number of hours men devote perweek to hOuseworkis normally distributed with a mean of 16 hours and a standard deviationof 3.5hours. What is the probability that a randomly selectedman ~ds more than 20hours perweek to housework? ~.127~ B) .2379 q .6276 .. D) .3729 E) .8729

~l ~ '/7...0 ') ~ pl ~ ""'7 \ .. \~) ~ •\'2..1 \ • According to a study, men devote an average of 16hours per week to housework.Assume that the 38) _

number of hours men devote per week to housework is normally distributedwith a mean of 16 hours and a standard deviation of,3.5 hours. Suppose that the 10%of men who spend the least time ~usework devote £ewer than x hours per week to housework. Find x. (.J!' 11.52 B)15.12 q 20.48 D) 12.52 E) 11.25

5

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Area Under Standard Normal I

Distribution P(O<Z<z)

, .. .. . . . .! . . .� z· 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09�

0.0 0.0000 0.0040 0.0080 0.0120 0.~60 0.0199 0.0238 O,027t 0.031' 0.0359 0.1 0.OS98 0.0488 0.G478 0.0517 0.055T 0.0st8 0.0836 0.0875 0.0714 0.0763 0.2 0.0.,93 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1084 0.1103 0.1141 0.3 J).1178 0.1217 0.1265 0.1283 0.1331 0.1. 0.1406 0.1443 0.1480 0.1617 0.4 O~16$4 0.1591 0.16ae 0.1664 0.1700 °ll 0;1172 0.1808 0.1844 0.1878 0.6 0.181$ ,0.18SO 0.1. 0.2018 0.2054 .0. 0.2123 0.2187 0.2180 0.2224 0.6 0.2281 0.2324 0.2357 ,0." O.24~ 0.24$4 0.2486 0.2617 0.2M90""0.7 0••0 0.2611 0.2$42 0.2673 0.2704 0.2734 0.2764 0.2784 0.2823 O.aBU 0.8 0.2881 0.2910 0.2839 0.2867 0.2985 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 O.~212 O.32J8 0.3284 0.3,288 0.3316 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.34$5, 0.3S08 0.3531 0.36$4 0.35T7 0.3599 0.3621 1.1 0.3843 0••66 0~3886 0.3708 0.37_ 0.3749 0.3170 0.3190 0.3810 0.3830 1.2 0.3849 0.3868 0.3888 0.3907 0.3925 0.3944 0.3982 0.3980 0.3197 0.4015 1.3 0.4032 0.4048 0.4066 0.4082 0.4089 0.4115 0.4131 0,4147 0.4162 0.4177� 1..4 0.4182 0.4a07 0.4222 0.4236 0.4251 0.42'6 0.4279 0.4292 0.4306 0.4319� 1.6 0.4332 0.4345 0.43~7 0.4370 OA3Jl~ 0.4394 0.4406 0.4418 0.4428 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4496 0.4506 0,4516 0.4626 0.4536 0,4545 1.7 0.4554 0.4664 0.4573 ,0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4849 0.4856 0.4664 Ct.4671 0.4678 0.4686 0.4693 0.4699 0.4106 1.9 0.4713 0.4719' 0.4726 004732 0.4738 0.4744 0.4760 0.4766 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4330 0.4834 0.4838 0.4842 0.4848 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0,4878 0,4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0-4.918 . 0.4920 0.4922 0.4926 0.4927 0.4929 0.4931 0.4932 0.4934 0,4936 2.5 0,4938 0.4$40 0!4941 0.4943 0.4946 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4965 0.4956 0.4957 0.4959 0.49$0 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4986 0.4886 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.49~0

3.1 0.4$90 0.4t91 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.2 0....93 0.499.3 0.4994 004994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 3.3 0.4995. 0.4$95 0.~95 0.4986 OAt96 0.4$96 0.4996 OAt96 0.4996 0.4997�

.. 3.4-- 0.4891-, ~.4997 -O.499J- -.GAtt ~ O.49lJ· -0.4881- -0A987 .0.4981 ·-0.4988­3.S 0.4988 0.4998 0.4988 0.~98 0.4998 0.4198 0.4988 0.4998 0.4998 0.4988�

3.6 0.4998 0.4998 0.4999 0.4999 0.4988 0.49'99 0.4999 0.4999 0.4999 0.4999 3.7 0.4998 0.4999 0.4999 0.4999 0.4989 0.4999 OMts 0.4999 0.4999 0.4199 3.8 0.4999 0.4999 0.4999 004999 0.4999 0.4999 0.499S 0.4998 0.4$89 0.4989 3.9 0.8000 0.6000 0.5000 0.6000 0.6000 0.6OCtCt 0.1000 0.5000 0.5000 0.8000

4.0 0.6000 0.5000 0.5000 0.6000 0.6000 0.5000 0.6000 0.5000 0.6000 0.5000 - ,

60