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? [2 marks]

c.List all possible samples of size 2 and calculate the mean of each sample. [4 marks]

d.Graph a probability histogram of the sample means. Title this graph: Sampling Distribution of Sample Means. What is the shape of the histogram? [2 marks]

e.Find the mean, variance, and standard deviation of the sample means. [3 marks]

f.Compare your results from (a) and (e). What do you notice? [2 marks]

g.Compare the shapes of the probability histograms in (b) and (d). What do you notice? [2 marks]