A population consists of 5 units: X = 5, 7, 9, 11, and 13. All units are given equal probability of selection and a sample of size 2 is selected with replacement. Use the Central Limit Theorem to answer part (e) below.

a.Compute the population mean (), population variance (2), and population standard deviation ().

[3 marks]

b.Graph a probability histogram of the population values. Title this graph: Population Distribution. What is the shape of the histogram?

c.List all possible samples of size 2 and calculate the mean of each sample.

d.Graph a probability histogram of the sample means. Title this graph: Sampling Distribution of Sample Means. What is the shape of the histogram?

e.Find the mean, variance, and standard deviation of the sample means.

f.Compare your results from (a) and (e). What do you notice?

g.Compare the shapes of the probability histograms in (b) and (d). What do you notice?