Assume a population of 1,2, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below.

1,1 1,2 1,12 2,1 2,2 2,12 12,1 12,2 12,12

a. Find the value of the population standard deviation.

b. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations.

c. Find the mean of the sampling distribution of the sample standard deviations.

d. Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?