Answer
a.
Mean, probability:
46, 1/16
47.5, 2/16
49, 1/16
51, 2/16
52, 2/16
52.5, 2/16
53.5, 2/16
56, 1/16
57, 2/16
58, 1/16
b. 52.25
c. Yes, they are.
Work Step by Step
a. We know there are 4 numbers, so there are $4^2=16$ ways to combine them. Combining the values with the same mean, we obtain the following:
46, 1/16
47.5, 2/16
49, 1/16
51, 2/16
52, 2/16
52.5, 2/16
53.5, 2/16
56, 1/16
57, 2/16
58, 1/16
b. We know that the mean is equal to the sum of all of the values, each multiplied by their respective probability of occurring. Thus, we see that the mean is 52.25.
c. Yes, they do. Sampling means are intended to be close to the population mean, so they are good estimators of what the population mean will be.
