Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 18 and a standard deviation equal to 5. (a) Describe the shape of the sampling distribution of the sample mean x. Do we need to make any assumptions about the shape of the population? Why or why not? , because the sample size is (b) Find the mean and the standard deviation of the sampling distribution of the sample meanx. (Round your answer to 1 decimal place.) FAR OX (c) Calculate the probability that we will obtain a sample mean greater than 20; that is, calculate P(x > 20). Hint: Find the z value corresponding to 20 by using u; and a; because we wish to calculate a probability about x. (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)

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