Retail stores experience their heaviest returns on December 26th and December 27th each year. The distribution for the Number of Items Returned (X) for Hilldale Macy's on those days last year is given in the table below. It has mean: μ = 2.61 and variance 2 = 1.80 Assume the probability distribution also holds for this year.

Number of Items Probability

1 0.25

2 0.28

3 0.20

4 0.17

5 0.08

6 0.02

(a) In this year, a random sample of size 45 returns is selected for review. Describe the sampling distribution of the sample mean (shape, center, and spread).

(b) What is the probability that the sample mean will be greater than 2.9 items?

(c) Find an upper bound b such that the total number of items returned by 45 customers will be less than b with probability 0.95.