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problemset5 - after 290 days b Births with gestation time...

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PAM 2100 Lecture 1 Fall 2008 Problem Set #5 Posted: October 23 rd , 2008 Due Date: Tuesday, October 28 th , 2008, in class 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? b) What is the probability that the repair shop receives at least three repair calls during an hour? #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
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Unformatted text preview: after 290 days? 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? #3) Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)} (disregarding order). Let X be the sum of the two balls selected. a) Write down the probability distribution of X. b) What is the probability that the sum is at least 4? c) What is the mean of X ? #4) Solve problem # 4.74 from the textbook....
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