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1 1.ray L - JC D stistics & Probability,. += -,-2%,- Exam #1 (Chapters 1-6) 3 Please Show Work, when possible! (If you don't, I can't give you partial'credit!) 1. In June 2003 Consumer Reports published an article on some sport-utility vehicles they had tested recently. They reported some basic information about each of the vehicles and the results of some tests, e co9ted by their staff. told the b&d - and nage of each vehicle, its price and whe er it had transmission. They reported the vehicle's fuel 2 economy (in m~les per of seconds to go from zero to 60 mph), and its braking distance (in feet) to stop from 60 mph. a) List the yar.iables and indicate whether each variable.-- is categorical or quantitative. If the variable is quantitative, state the units. # w* b) Are any of the variables identifiers? If so, which one(s)? w - Na- -5 i&h% ~ n i q * ~ ~ &- -4-i- &I& W3-b,*a-me w... -,- took a big test, and the highest score was 92. When the tests were discovered a grading error. After correcting the error, score that student's score made each of these summary statistics fran 4a * 95 a) Mean INC~QCQS~V b) Median!h& , ', c)- Range klwed IQR gffrycd w e) Standard deviation \~C&%4d

2 ro determine if people's preference in dogs had changed in recent years, organizers of a local dog show asked people who attended the show to indicate which breeds was their favorite. This information was compiied by dog breed and gender of the people who responded. The table summarizes the responses. 5i Do you think the breed selection is independent of gender? Give statistical evidence to support your conclusion. Please explain clearly what statistics you are referring to and explain what these statistics mean. - wx/.m,= g~rn-~ - afhw L F&C\ >v-

3 4; The boxplots show prices of used cars (in thousands of dollars) advertised for sale at three local different car dealers. 20t T Ace Buylt Car2 Dealer a) Which dealer offers the cheapest car offered, and at what price? Explain for partial credit. & &-pyice OF &&fr;;m.,/ b) Which dealer has the lowest median price, and how much is it? Explain for partial credit. -@y9it af LL &t& #Io,m#(/ Ace-~orfh &4 r'qe ot Ate = -&I 10 CN~E c) Which dealer has the smallest price range, and what is it? Explain for partial credit. 41 )o,w. If ( ~ Ilp-5=/1 3 d) Which dealer's prices have the smalles IQR, and what is it? Explain for partial credit. &Z wi* ajl rn OF Q3-Q, = IV-11=3 e, Which dealerpeneralll' sells cars cheapest? Explain for partial credit. ie btcu6~ rf. +he lowest rndm amd J

4 a&; 5. The World Almanac and Book of Facts 2004 reported the percent of people not covered by health insurance in the 50 states and Washington, D.C., for the year Computer output gives these summaries for the percent of people not covered bv health insurance: a) Were any of the states outliers? Explain how you made your decision. a, - ltrld&: 1o.g -$-gs-- /Ah- (b, 7 C <,857 7 Z~~S-JC 83 + r.~-lw - A. 7 1 ~. 5 r Min Q1 Median Q3 Max Mean SD %arc y-. Ci,.r~$ I?%\' , ~b- o/.e ous(r!*w k ~ I"".& ts 2i:r -4 %?.. ' > = sc....-pump.ur+m * b) Is it mor~@~fo&iate' to dse the mean and standard deviation OR the median and IQR to describe these data? Explain, using the following histogram of the data: -- Histopramof % Mt covered 14 1

5 6.. Costs for standard veterinary services at a local animal hospital follow a Normal model with a mean $80 and a standard deviation of $20. i.'..i! b) Is it usual to have a veterinary bill for $125? Explain. C) ~'hat-i-s the IQR for the costs.of btandard veterinary services? Show your work. \

6 a W (12-1,. 05) 1 7. A machine that fills cans with soda fills according to a Normal model with a mean of 12.1 ounces and a standard deviation of 0.05 ounces. a) If the cans claim to have 12 ounces of soda each, what percent pf cans are under-filled? (meaning, on the can it is printed that there is 12 ounces of soda) Show work for partial credit! v;. a,' -., +..., *.,I:-) = - = \ s I.., 7:.,, ':' -..., I.. 2 r ~ \ '- - I ; I <; -.-.:.- VCWUI~ filled yd ) U M ~ ~ V I J,I -,G.+ 'L.?. 2-b+ sj,a :; '~;~;,;i'l~~'d ta 7 +$I-!'li :2 ; 11,,i: ' &$i 4.,: :.;,,.,. ; 55.: ;.$.- 4. &f".,. :.**: v* - 6:,*.. a-' I.,pi * ' -.. i--* -,- <-. - c ' id - ;A.,... L < --..L:. a -.. b) Management wants to ensure that.only 1 % of cans are under-filled. If the meai"fil1 of the &ins " remains at 12.1 ounces, what standard deviation does the filling machbie need to have to achieve this goal? Show work for partid credit! \ -<2.; ~;,.-A c) What does it mean to reduce the standard deviation, in this context? Wh~n the shnduvd devlahon 1s f~duced ran hllln more3 bccomrs pccuvate, pm&mn 3 th& \&he: J :cl&tc, C ~ ~ O U V cs + \M cans) ~q the set I~.,QQSC~. k.~ -)..- A 4-0 the meqn CdeS!v{d?f )- y w:r.-k- - v '; k-,. =.. 1? ;;;)w *?;-- -. ;.\ :..:.,k... I t:!-;-?.;?f - A' -<-A..&,+*.: :.'.:.-';.>.. 6: : -... J 4