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STA 301 - HW08

# STA 301 - HW08 - (a What is the probability that a random...

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STA 301 – Applied Statistics Spring 2008, Section B Homework #8 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 (b) the number of sample means expected to fall between 172.5 and 175.8 centimeters (c) the number of sample means expected to fall below 172.0 centimeters.

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STA 301-B, Spring 2008 Homework 8 Page 2 of 3 Question 2 (p. 252, #8.24 – modified) A certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms.
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Unformatted text preview: (a) What is the probability that a random sample of 36 of these resistors will have a combined resistance of more than 1458 ohms? (b) Your answer in part (a) is merely an approximation. What additional assumption is needed to provide an exact probability statement? (c) Which theorem indicates that our result in part (a) is reasonable, even without the additional assumption in part (b)? STA 301-B, Spring 2008 Homework 8 Page 3 of 3 Question 3 A random sample of size 100 is drawn from a normal distribution with mean 150 = μ and standard deviation 15 = σ . Find the probability that (a) the first member of the sample takes a value between 148 and 152. (b) the sample mean takes a value between 148 and 152....
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STA 301 - HW08 - (a What is the probability that a random...

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