A random sample of n= 64 observations is drawn from a population with a mean equal to 20 a...

A random sample of n= 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16.

a. Give the mean and standard deviation of the (repeated) sampling distribution of .

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b. Describe the shape of the sampling distribution of . Does your answer depend on the sample size?

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c. Calculate the standard normal z-score corresponding to a value of  = 16.

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d. Calculate the standard normal z-score corresponding to  = 23.

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e. Find P(x< 16).

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f. Find P(> 23).

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g. Find P(16< < 23).