STA 301 - HW08 Key

# STA 301 - HW08 Key - STA 301 Applied Statistics Spring 2008...

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-3 -2 -1 0 1 2 3 .1736 .0735 .7529 STA 301 – Applied Statistics Spring 2008, Section B Homework #8 - Key Due Friday, April 4 Question 1 (p. 252, #8.22) The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. If 200 random samples of size 25 are drawn from this population, determine (a) the mean and standard deviation of the sampling distribution of X In the population we have and . Since we are taking samples of size n = 25, we have: and (b) the number of sample means that are expected to fall between 172.5 and 175.8 centimeters First, we find the probability of the sample mean falling between 172.5 and 175.8: Now, let Y be a random variable representing the number of our 200 samples of size 25 that have means between 172.5 and 175.8. Then Y is binomial with 200 trials and probability of success .7529. The number of sample means expected to fall between 172.5 and 175.8 is therefore: 200 * .7529 = 150.58 5 . 174 = X μ 9 . 6 = X σ 5 . 174 = = X X μ μ 38 . 1 25 9 . 6 = = = n X X σ σ ( ( 29 ( 29 ( 29 7529 . 1736 . 0735 . 1 94 . 45 . 1 1 94 . 45 . 1 38 . 1 5 . 174 8 . 175 38 . 1 5 . 174 5 . 172 8 . 175 5 . 172

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