The diameter of a brand of? Ping-Pong balls is approximately normally? distributed, with a mean of 1.31 inches and a standard deviation of 0.08 inch. A random sample of 16 ?Ping-Pong balls is selected. Complete parts? (a) through? (d).

a. What is the sampling distribution of the? mean?

A. Because the population diameter of? Ping-Pong balls is approximately normally? distributed, the sampling distribution of samples of 16 will not be approximately normal.

B. Because the population diameter of? Ping-Pong balls is approximately normally? distributed, the sampling distribution of samples of 16 will also be approximately normal.

C. Because the population diameter of? Ping-Pong balls is approximately normally? distributed, the sampling distribution of samples of 16 can not be found.

b. What is the probability that the sample mean is less than 1.28 ?inches?

P(Upper X overbarXless than<1.28?)equals=.

?(Round to four decimal places as? needed.)

c. What is the probability that the sample is between 1.28 and 1.32 ?inches?

P(1.281.28less than

?(Round to four decimal places as? needed.)

d. The probability is 57?% that the sample mean will be between what two? values, symmetrically distributed around the population? mean?

The lower bound is [ ] inches =

?Round to two decimal places as? needed.)

The upper bound is [ ] inches =