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 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 mean x (Round your answer to two decimal places):
(c) Calculate the probability that we will obtain a sample mean greater than 25; that is, calculate P(x > 25). Hint: Find the z value corresponding to 25 by using z-score formula because we wish to calculate a probability about x: (Round probability to four decimals)
P(x > 25)
(d) Calculate the probability that we will obtain a sample mean less than 21.567; that is, calculate P(x < 21.567) (Round probability to four decimals)
P(x < 21.567)