The diameter of a brand of tennis balls is approximately normallydistributed, with a mean of 2.59 inches and a standard deviation of 0.05 inch. A random sample of 12 tennis balls is selected. Complete parts(a) through(d) below.

a. What is the sampling distribution of themean?

A. Because the population diameter of tennis balls is approximately normallydistributed, the sampling distribution of samples of size 12 will also be approximately normal.

B. Because the population diameter of tennis balls is approximately normallydistributed, the sampling distribution of samples of size 12 cannot be found.

C. Because the population diameter of tennis balls is approximately normallydistributed, the sampling distribution of samples of size 12 will be the uniform distribution.

D. Because the population diameter of tennis balls is approximately normallydistributed, the sampling distribution of samples of size 12 will not be approximately normal.

b. What is the probability that the sample mean is less than 2.56 inches?

P(X<2.56)=

(Round to four decimal places asneeded.)

c. What is the probability that the sample mean is between 2.57 and 2.61 inches?

P(2.57

(Round to four decimal places asneeded.)

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

The lower bound is inches. The upper bound is inches.

(Round to two decimal places asneeded.)