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.
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. Hence we can 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.
