Suppose that we will randomly select a sample of 59 measurements from a population having a mean equal to 22 and a standard deviation equal to 9.

(a)Describe the shape of the sampling distribution of the sample mean

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

(b)Find the mean and the standard deviation of the sampling distribution of the sample mean

.(Round yourxxanswer to 1 decimal place.)

(c)Calculate the probability that we will obtain a sample mean greater than 25; that is, calculateP(

> 25). Hint: Find thezvalue corresponding to 25 by using and because we wish to calculate a probability about .(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.)

(d)Calculate the probability that we will obtain a sample mean less than 21.567; that is, calculateP(

< 21.567)(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.)