Identify the probability of each sample, and describe the sampling distribution of the sample means.
-The number of books sold over the course of the four-day book fair were 189, 167, 271, and 83. Assume that samples of size 2 are randomly selected with replacement from this population of four values.

A) $1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16$
B) $1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16$
C) $1 / 2 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 2 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 2 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 2 ; 1 / 16$
D) $0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 1 / 16 ; 0 / 16 ; 1 / 8 ; 1 / 16 ; 1 / 16 ; 1 / 8 ; 1 / 16 ; 0 / 16 ; 1 / 8 ; 1 / 16$

Question

Identify the probability of each sample, and describe the sampling distribution of the sample means.
-The number of books sold over the course of the four-day book fair were 189, 167, 271, and 83. Assume that samples of size 2 are randomly selected with replacement from this population of four values.

A) $1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16$
B) $1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16 ; 1 / 16$
C) $1 / 2 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 2 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 2 ; 1 / 16 ; 1 / 4 ; 1 / 16 ; 1 / 2 ; 1 / 16$
D) $0 / 16 ; 1 / 16 ; 1 / 8 ; 0 / 16 ; 1 / 16 ; 1 / 8 ; 1 / 16 ; 0 / 16 ; 1 / 8 ; 1 / 16 ; 1 / 16 ; 1 / 8 ; 1 / 16 ; 0 / 16 ; 1 / 8 ; 1 / 16$

Quizplus · Accepted Answer

Since each sample of size 2 is selected with replacement from a population of 4 values, there are 4x4=16 possible samples. Each sample has an equal chance of being selected, making the probability of each sample 1/16.