CHAPTERS 5 & 6. Nan:-e: ~t.th:()il')..

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1 Math 123, Fall 16, Midterm 3 Instructor: Saba Gerami CHAPTERS 5 & 6 Nan:-e: ~t.th:()il').. Total: 90 Points Directions: Show all your work. You only receive half of the points if you do not explain your reasoning. You can use a graphing calculator. You may not use cell phone. or notes. Round to two decimal places. 1. Find the area of the indicated region under the standard normal curve. (4 points) ' '0.8 0 a) b) 2.. t '..,'. (4 points) a) Write two differences between a normal distribution and the standard normal distribution. -rtu.k ft, \. QAt tut- ~S~(~ '~~Mt.. Thtt r: ~' S (jjj_ tto t- ~(~ -ftu. SiJ\W\.l.. b) Write two similarities between a normal distribution and the standard normal distribution. '80~ 411(. ~ft,. fjij.., bef/~'. ~ ~ ~tt\t fri L 3. Find the indicated area under the standard normal curve. (6 points) 1 a) To the left ofz ==

2 b) To the right of z = ().O\O~ -2.:~O c) Between z = 0.5 and z = ::-D.~Z"~ ~d).)" --.IIJ O.bq,~ 2.~I ~j -.J), j " 1_ f).ofo'1- O ")3So.tl-?-;5-:'0.(P, If c:- 0, 2' 2.() c) To the left of z = 0.64 or to the right of z = 2.6 ~..'Z-." _ ~ ~::: (). "fqr3 ~ e~'~~.._,twr=o.13g~ O.(,t.( Z.e"..-~--:::-()--:::. ~;:-'::3~gdJ:'-'t-()-. b---::t)lff~..-o-::.-q.:7.q=-3 4. In a study of bumblebee bats, the weights were normally distributed with a mean 1.8 grams and a standard deviation of 0.33 gram. Find the probability that a randomly selected bat weighs: a) more than 2.3 grams. )A.,:::;-,.BI ~,I: ). "3~ (6 points),.. I -) I_~' or,r3 ~ o.oot]: '--'1 ~. &~ ~ '/.. - j). '" z. 3-,.<t... ~ - o 3'!> b) between 1.0 and 3.2 grams.

3 a) 5. Find the z-score that corresponds to the followi 0.1 '~ 1;-:. -I.2~ percentile. (4 points) b) P Scores for Bar exam were normally distributed with a mean of 135 and standard deviation of 12 in An agency only hires applicants with scores in the top 10%. Bardo is graduating from a law school soon. What is the lowest score he can earn in order to be eligible to be hired by the agency? (4 points) 7. The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. (6 points) n=19 p=0.23 q=o.77 a) Can the normal distribution be used to approximate the random variable x? Explain your reasoning. t1p: ("I ( 0-1.3):::: if -3"?- I s: n};;- IOf(o~11 ):/Cf-fo 3- tjot 110 rwj_ 3 to

4 b) A binomial probability is given: P(x = 116) Use a continuity correction to convert the binomial probability to a normal distribution probability. p('is.r( X < "".s) qat:\\()i..\, I. L J of- c) Find P(x = 116). \ipfs ~'S(),i"'"-In S'fWNItUS ufl'to eli, : ~::; X- Jf = II"of. ~ r~- or 1.93 ;(o The annual per capita waste of food from supermarkets is normally distributed with a mean of pount!! and standard deviation of 35.5 pounds. Random samples of 40 C!,redrawn from fi.=' g r. 2.. th,s population, and the mean of each sample is deterrmned. (6 points) a) Use the central Limit Theorem to find the mean and standard deviation of the following sampling distribution of sample means. 0"'= 3S-.r V",:;;qo tr/ _ /J;. - b) What is the probability that the mean value of wasted food from supermarkets is more than 250 Ibs annually per capita? P( i)~~o) = P("&) ti ~'1);C' 1_{).~tf'8~l~ f')()02] r :0- K f{x = Jg) - (Z)-~ ~ /1. t;,-/ s.u 4

5 p=() }"z /' ~:~ig )A.:: np :::Z3. tf o-~j~fht :::3.3~ 9. A survey found that 52% of AHC students sells their book back to the bookstore. You randomly select 45 AHC students ages and ask them whether they do that or not. (6 points) a) Use a continuity correction to find the probability that the number who sell their books backs is less than or equal to 30. P(x 30) = PC)( < 3OS):::: P(b-<"2.'2.)~_' "930 I ~ ~ ~ X -,M ::.30.r-- Z3.l/ Z 2 12 (J"' 3. 3).. b) Use a continuity correction to find the probability that the number who sell their books backs is greater than 40. ~ HA~t~,~ PC '()tfo) = P( 't> los) = p(~ > 5. fo) O ""'B == I-D. qqor g:::- ()0 0 ()2 10. Find the following values for the given confidence level c. a) t, and -tc when C = 90% and n=28. b) Z; and -Zc when C= 98% O~.ol (4 points) -!J -/; C -:::,.103 -ic z: o.ch! Iw~.&.IIi-It-o\--.-~._s... DWL ~ L o 0 2. _ 0.0, -2- '!>'3 2-! For the same sample statistics, which level of confidence would produce the widest confidence interval? Choose the correct answer below. 1)<Qo%, because as the level of confidence decreases, Z; decreases. CD 99%, because as the level of confidence increases, z; increases %, because as the level of confidence increases, Zc dec~s. 2.~%, because as the level of confidence decreases, Z; increases. (2 points)

6 12. You construct a 95% confidence interval for a population mean using a random sample. The confidence interval is 24.9 < J.l. < 31.5 Is the probability that J.l. is in this interval 0.95? Choose the correct answer below. (2 points).. AillJilfu<lllll 1. Yes. The probability that J.l. is in this interval is o. a large number of samples are taken the probability that the mean is in the interval is No. Approximately 95% of the sampled data will fall in the confidence interval. For problem 13 15, number your steps as in your formula sheet to receive full credit,,~~~ 13. The mean room and board expenses er year at four-year colleges is among 100_"";? students. Construct a 98% confidence interval for popula ion mean. Assume room and board expenses have standard deviation of$1300 based on recent studies. E.iJt,~0 CD. Wi~ SiI-'"f't- ~~ / () r1:::i()o '430 V (i) X:;; r~/qoo d) u.;or~ +wo'-"f:;- f_o.qb~o.02 ~ C)nt./.J'/::O.()2 :;;().Ol Z -2c;:ZJ1 s.;t. '3 ~ (12 points) 'isb X ==-'S;<.fo-o t'\= (00 &) E:: ~ c. g:_::;; 2.331' : 302."I ~ ~ It;",'foO-j02.Q <)A -: 1S(<<fOcJ.f l~1)"'1., <JA.< L"702.'1 6 J ~'" qff. (JJJU M)A. ~ bw

7 I.~.- ~ 21-,d. -;I-Z?- S., == 3S'"'" /' '::: -~ Y 14. In a survey of 35 students in Saba's statistics course, 27 said that they absolutely love 3)" 3S""' listening to Disney music during worksheet hours! Construct a 95% confidence interval for the population proportions of students in all Saba's courses who absolutely love listening to Disney music during worksheet hours. (12 points) I) " ~r " g n~'.j) I Xc P..'7I p.:: 3f I 't~~ [).) np;: 3)(2:t ) '\ (9 ) -V' # ~ 1- >" ) v' 1-1~ :;- 3) -g'"~~_8 ~_S~----.::~ 1) r) ~T J)rJ1< P<U 0./3"?) O.O~ -Ir.oIo ~:r='-d.,);:o."r? 1'f' 3) ~ ~ 'DHt f-,f= ~ ~ o.os: 0 "b 3 <P< 0 ql -2.c.:' -I.llb "'z.c:/.'t, 2-" s ) r. A~ q~i..eri,'u s: ~c(~)::; ','t'(!~'fi:. ~ O.l3,? ~ p~ (fi(j 0",,3 ~o,t1[1 JI'1 't) 15. You randomly select 16 coffees and measure their temperatures. You get an average of 162 r'i==- '" Fahrenheit and a standard deviation of 10 Fahrenheit. Construct a 80% confidence interval fo~~iti.tiji_ the population's mean of coffee's temperature. Assume the temperatures are normally...,.. 'C. distributed. (12 points) X.:::1'2 (!Jw.;k6".tt..(f) s:::i 0-2. 'i-::: I (g 2. J $.::'10,.,))=-'b-'d~. ior: i.e" ( 3'(1 -f;c. ~c. -ic.::; -I 3'(/