The number of books sold over the course of the four-day book fair were 190, 100, 272, and 74. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Identify the probability of each sample, and describe the sampling distribution of the sample means.

the answer is below

Step-by-step explanation:

We have the total number of possible samples = 4 * 4 = 16 (As 4 choices for each value)

in addition we have to as all sample occur with equal probability, probability of each sample = 1/16, below is samling distribution of mean

x1x2probabilityP(x1,x2)sample mean

190190    1/16                 190

190100    1/16                 145

190272    1/16                 231

19074    1/16                 132

100190    1/16                 145

100100    1/16                 100

100272    1/16                 186

10074    1/16                        87

272190    1/16                 231

272100    1/16                 186

272272    1/16                 272

27274    1/16                 173

74190    1/16                 132

74100    1/16                 87

74272    1/16                 173

7474    1/16                 74

Summarizing above with adding duplicate values

sample mean   probability

       74              1/16

      87               1/8

    100                1/16

    132                1/8

    145                1/8

    173                1/8

   186                1/8

   190               1/16

    231               1/8

   272               1/16