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 3': . Do we need to make any assumptions about the shape of the population? Why or why not? I_ .becausemesamweslms _ (In) Find the mean and the standard deviation of the sampling distribution of the sample mean i . (Round your of answer to 1 decimal place.) 1: xi (c) Calculate the probability that we will obtain a sample mean greater than 20; that is, calculate P( i > 20). Hint: Find the zvalue corresponding to 20 by using u i and a i because we wish to calculate a probability about 3? . {Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round 2-scores to 2 decimal places.) we) (d) Calculate the probability that we will obtain a sample mean less than 17.564; that is, calculate PI 3':