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Answer+Key+to+Assignment+1 - Econ 15B UC Irvine Assignment...

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Econ 15B Assignment 1 Ghosh UC Irvine (Total 50 points) Due 08/10/10 Chapter 9: 9.5 (8 th edition): (10 points) A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population? ANS: The sampling distribution of the mean is normal with a mean of 40 and a standard deviation of 12/ 100 = 1.2. 9.10 (8 th edition): (10 points) Given a normal population whose mean is 50 and whose standard deviation is 5, a. find the probability that a random sample of 4 has a mean between 49 and 52. b. find the probability that a random sample of 16 has a mean between 49 and 52. c. find the probability that a random sample of 25 has a mean between 49 and 52. ANS: a. = < < ) 52 X 49 ( P < σ µ < 4 / 5 50 52 n / X 4 / 5 50 49 P = P(–.40 < Z < .80) = P(Z < .80) − P(Z < −.40) = .7881 −.3446 = .4435 b. = < < ) 52 X 49 ( P < σ µ < 16 / 5 50 52 n / X 16 / 5 50 49 P = P(–.80 < Z < 1.60) = P(Z < 1.60) − P(Z < −.80) = .9452 −.2119 = .7333 c.
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