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problemset5solution

# problemset5solution - PAM 2100 Spring 2009 Problem Set#5...

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PAM 2100 Spring 2009 Problem Set #5 Answer Key Total Points: 10 Round your final answers to four decimal places, if necessary. #1) Let the random variable X be the number of repair calls that an appliance repair shop may receive during an hour. The distribution of X is given below: Value of X 0 1 2 3 4 Probability 0.3 0.12 0.18 0.2 a) What is the value of the missing probability? (0.5 points) Ans. 0.2 b) What is the probability that the repair shop receives at least three repair calls during an hour? (0.5 points) Ans. 38 . 0 2 . 0 18 . 0 ) 3 ( = + = X P #2) It has been established that the length of gestation until birth for pregnant women is a random variable that is well modeled by the Normal distribution with a mean μ = 282 days and standard deviation σ = 11 days. a) What is the probability that a randomly selected pregnant woman will give birth after 290 days? (0.5 points) Ans. Here, x=291. The standardized value of x is (291-282)/11=0.82. In Table A, the area to the left of z=0.82 is .7939. So the area to the right of z=0.82 is (1-.7939) =.2061 (It is the proportion of women that give birth after 290 days, therefore it is also the probability that a randomly selected woman will give birth after 290 days). (Note, if someone uses x=290, consider that as correct answer as well, in that case the answer is .2327) b) Births with gestation time of 258 days or less are considered to be premature births. What is the probability that a randomly selected pregnant woman will give birth to a premature baby? (0.5 points)

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Ans. Here, x=258. The standardized value of x is (258-282)/11=-2.18. In Table A, the area to the left of z=-2.18 is .0146.
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