The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.71 inches and a standard deviation of 0.05 inch. A random sample of 12 tennis balls is selected.

a. What is the sampling distribution of the mean?

1. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 12 cannot be found.

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

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

4.Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 12 will be the uniform distribution.

b. What is the probability that the sample mean is less than 2.70 inches?

P(X<2.70)=____

(Round to four decimal places as needed.)

c. What is the probability that the sample mean is between 2.69 and 2.73 inches?

P(2.69

(Round to four decimal places as needed.)