SOLUTION: Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why

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Question 591992: Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The sample standard deviation is

(n is the sample size)



The definition for "unusual" varies, but it usually indicates data lying roughly 1.96 standard deviations away from the mean (i.e. outer 5% of data). The corresponding value for z=1.96 is



115 lies within the middle 95%, so it would not be deemed "unusual."