The number of books sold over the course of the fourday book

The number of books sold over the course of the four-day book fair were 152, 173, 294, and 65. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Identify the probability of each sample, and describe the sampling distribution of the sample means.

Solution

The possible samples is

(152, 152) ,(152,173), (152,294), (152, 65)

(173, 173), (173, 294), (173, 65), (173, 152)

(294, 294),( 294, 65), (294, 152), (294, 173)

(65,65) (65,152), (65, 173), (65, 294)

So, there are 4^2=16 possible samples with replacement, each with probability is 1/16

Then we calculate the mean of each sample is 152, 162.5, 223, 108.5, 162.5, 173, 233.5, 119.5, 223, 233.5, 294, 179.5, 108.5, 119, 179.5, 65

and that would be the sampling distribution of the sample means.