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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?
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Explanation & Answer
Solution:
Sx = SD/root(sample)
Sx = 15/root(3) = 8.6602
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."
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