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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 oneyear life insurance policies with a face value of $100,000 to 25
yearold 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.O2J! 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) XSC (gt13" 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 AzlVM «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
,(szb _ ° 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; WWYW 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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 Spring '08
 PamelaSatterfield

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