exam2a06S_sol - MATH23O Spring 2006 Exam 2a Name: K0 ¥ Z...

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Unformatted text preview: MATH23O Spring 2006 Exam 2a Name: K0 ¥ Z Section: Instructions: 1 2. mwew . Do not start until instructed to do so. You may use a calculator and one 3x5 card (front and back) with notes, but nothing else. SHOW ALL WORK to receive full credit. Clearly indicate your answers. Report answers that are probabilities to 4 decimal places. . The work you turn in must be your own. 1. 8 points A couple plans to have children until they have a girl, but they agree that they will not have more than three children. Assume boys and girls are equally-likely and that births are independent events. Let X = number of boys they’ll have. Find the probability density function of X. f(x). 2. 8 points Let S = {10,20,60} and let ;1 = average of the numbers in S . An experiment consists of randomly selecting two numbers from S without replacement (a simple random sample). Let Y = arithmetic mean of the two numbers. Show that E (Y ) = y . [074/0 +é0 :1 SO E ii VJ 3. 12 points A cereal manufacturer puts pictures of famous athletes on cards in boxes of cereal in the hope of increasing sales. The manufacturer announces that 20% of the boxes contain a picture of Tiger Woods. Suppose you buy boxes of this cereal at random and independently. How many boxes must you buy to have at least a 95% chance of finding at least 1 picture of Tiger? Show your work. @emoJ/l f PM [€53 4. 8 points Tuberculosis (TB) is a fairly rare disease with only about 5 cases per 10,000 people in the United States. Suppose a test for TB performs such that 99.9% of those with TB will test positive and 1% of those who do not have TB will test positive. What is the probability that someone has TB given that they test positive? FF(7/B>; , 0009 10r(+/T5> 1" ,2??? “\x p/(+/77g>)7>r(~,-g) +pr(+/T6’)Pr(m ) .9$7(KWV) /_______________________.. ,?99[,d003') #- ,Dl(-7??5> {I = [#0475 / Questions 5 — 7: A tennis player makes a successful first serve 55% of the time. Assume that serves are independent events. Consider a sequence of 6 first serves and let X = number of successful first serves. 5. 2 points Find y =E(X). M :’ :1 [1p 3 @701“ g. g 6. 2points Find 0' =1lVar(X). V: /np<).,f\ : IIZIES/o 7. 5points Find Pr(|X—,u|>20'). {H )X/ag) > 2.967) : Pr (x =0 or X : é) : propa) + Fr{)(:é) 2 Mtg/omfcm" + C(é/e/CSSJ‘Crs-J‘ d [03qu / V \ 8. 5 points Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests. Are these two tests given independently? fl' : imam +€S+‘ 8 > b/odai 7L¢S+ 9 FHA/i8) : PrMVMM ,2; = (723)636) N0! 77% fesfi wt ,2; # ,28’03 mi 3M4 mJe/Am/enfi/. ...
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exam2a06S_sol - MATH23O Spring 2006 Exam 2a Name: K0 ¥ Z...

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