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Exam 3 Key - Spring 2008

# Exam 3 Key - Spring 2008 - Finite Math Exam#3 Spring 2008...

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Unformatted text preview: Finite Math Exam #3 Spring 2008 Chapters 8, 9 & 10 Name Show all your work on this paper. Solutions without correct supporting work will not be accepted. 1. A check of 50 calculators just off the assembly line reveals that 5 have faulty cases, 8 have faulty batteries, and 3 have both of these defects. What is the probability that a randomly selected calculator from the collection will have a faulty case or a faulty battery? (6 points) I «931’ P(FCm PB) : 15%— : ”5"- L10 2. An insurance company is going to sell one-year life insurance policies with a face value of \$100,000 to 25- year-old women for \$1100. The company’s mortality tables show that these women will live for one year with a probability of 0.99. Consider the company’s eaming from such policies to be values of a random variable. Find the company’s expected earnings per policy. (8 points) E00: HOO(.OICD - 100,000600 :: lgq 3. Among 20 automotive CD players, 4 are known to have a defect. A sample of 3 of these players is selected, without replacement and without regard to order, to be checked for a defect. What is the probability that all 3 will have a defect or all 3 will not have a defect? (8 pts) 403+ [1663 4!] .— 3003 ’ ”775—" “-‘f‘i‘m 4. One card is drawn from a deck of 52 cards. What is the probability that the card is (4 pts each) a. A king, given that the card was a heart? T)( K \ H) 1: l [’3 l b. A diamond, given that the card drawn is a diamond or a heart? PtDl D all) “-— c. A diamond, given that the card drawn is a diamond and a jack? Pcutw '3') r l 3 d. What are the odds that the card is a king? _,‘l..._._’_.——- J...- .1..— "PLKU— 52 ~ 13 odds :ﬂtléfd : .1 l2 l7.) 'PCthoxlcl 3% “T’s’ 5. A contractor buys bags of cement from two suppliers — Rodrigues’s Lumber and Builder’s Mart — and stores them in a warehouse. She buys 60% from Rodrigues’s and 40% from Builder’s Mart and, upon deliver, discovers that 2% of the bags from Rodrigues’s are damaged and 4% of the bags from Builder’s Mart are damaged. (5 pts each) a. Draw a tree diagram for these data. .02. p .l0 K gudDamaed b. For a randomly selected bag, what is the probability that it came from Rodrigues’s and was damaged? 'PCRaml 1)) z: .0002) =1.O|2J! c. For a randomly selected bag, what is the probability that it came from Rodrigues’s, given that it was damaged? .Oll POND) 3 Tigris—PB?) : .(0(.02)+,4(,0LD "'3 ,42857 6. Tests show that about 4% of the people who take a particular drug are subject to side effects. (5 pts each) H520 3 P=.O4 ,‘b?.q(p a. Of 20 people taking the drug, what 18 the probability that no more than 2 will experience the side effects? 0 gen 34>ch + 1 sad; er + 2 stat 2515102; 1? 190C.o®°(.%)w+ “00043641053 MCLCMM‘M) ~ b. If 20,000 people take the drug how many people would you expect to experience the side e - .04 (20,000) 2] 900 Q0 l 7. A sample of 70 calculator batteries were tested for length of life. The results were as shown in the table: a. Estimate the mean. (5 pts) )7. = 7029+ Clara 1100+ 13(l3)l—ISCH) 0 b. Esti ..- I‘ dard deviat1on. (8 pts) X-SC (gt-13" Egg ’l—IMS’I M4310 4" 12, : 17?.Sl738’8 L ”l) M /0 £140.07 3.:4qt at up : s We! 1140.257 .0204 at It .308“; - A I340357 9.591 * ’3 56.701937 Az-lVM- «2.04 140,257 171W“ H : [\$8.802737 . . 5 T823714??? /éq’ 2 \$64 37333 LJW 12 to 14 ll 8. The weights of bags of Kay’s Potato Chips were found to be a normally distributed random variable with a mean of 6 oz and a standard deviation of 1A: oz. (4 pts each) _ A U 69 J 6 3 o 5 a. What percentage of the bags weighs less than 5 V2 oz? l 5 " O I 5. 8 7 Z b. What is the probability that a randomly selecte bag weighs between 5 1%. oz and 6 V4 oz? 2 - 154% _ 5 1% I .- I "" _ 0 -IS '5 ,(sz-b _ ° c. If a store has 500 bags of Kay’s chips in stock, about how many will weigh more than 7 oz? 9. The daily salaries of the Lhila Corporation employees are \$90, \$80, \$110, \$97, and \$70. These salaries have a mean of \$91 and a standard deviation of \$13.2. How many of the salaries lie within one standard deviation of the mean? (4 pts) [)1qu ,oselg.2. HowMﬂ/V‘é 1L; WW-YW low '5 131} 10. Assume that SAT verbal scores for a freshman class at a university are normally distributed with a mean of 520 and a standard deviation of 75. The top 10% 0f the students are placed in the honors program for English. What is the lowest score for admittance into the honors program? (8 pts) ,(y—S’LO 20:75 ﬁ/ﬂ/ﬂm WM z~vaj4wunlﬂ3dwwcfogagmmdaw g/ 2:LZ _ X—M z— 6 520 _ £;,_. ’12? -- ’75 X = (Mo was 8M 8cm gemtku ...
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Exam 3 Key - Spring 2008 - Finite Math Exam#3 Spring 2008...

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