## Elementary Statistics (12th Edition)

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.
a) We know there are 4numbers, 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.