Suppose we randomly select a sample of 64 measurements from

Suppose we randomly select a sample of 64 measurements from a larger population having a mean equal to 20 and a standard deviation of 4 .

a) Describe the shape of the sampling distribution of the sample mean x.

b) Do we need to make any assumptions about the shape of the population? Why or why not?

c) Find the mean and the standard deviation of the sampling distribution of the sample mean.

d) Can you find the probability that a single measurement will be greater than 21? If so, what is the probability?

e) Calculate the probability that we will obtain a sample mean greater than 21.

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