The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.71 inches and a standar

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The diameter of a brand of tennis balls is approximatelynormally​ distributed, with a mean of 2.71 inches and astandard deviation of 0.05 inch. A random sample of 12 tennis ballsis selected. Complete parts​ (a) through​ (d) below.
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Part 1
a. What is the sampling distribution of the​ mean?
A.
Because the population diameter of tennis balls is approximatelynormally​ distributed, the sampling distribution of samples ofsize 12 will also be approximately normal.
B.
Because the population diameter of tennis balls is approximatelynormally​ distributed, the sampling distribution of samples ofsize 12 cannot be found.
C.
Because the population diameter of tennis balls is approximatelynormally​ distributed, the sampling distribution of samples ofsize 12 will not be approximately normal.
D.
Because the population diameter of tennis balls is approximatelynormally​ distributed, the sampling distribution of samples ofsize 12 will be the uniform distribution.
b. What is the probability that the sample mean is less than2.70​ inches?
​P(X<2.70​)=enter your response here
​(Round to four decimal places as​ needed.)
c. What is the probability that the sample mean is between 2.69and 2.73​ inches?
​P(2.69<X<2.73​)=enter your response here
​(Round to four decimal places as​ needed.)
d. The probability is​ 56% that the sample mean will becentered between what two​ values, symmetrically distributedaround the population mean​ (so that​ 28% of the area isless than the mean and​ 28% is greater thanthe​ mean)?
The lower bound is
enter your response here
inches. The upper bound is
enter your response here
inches.
​(Round to two decimal places as​ needed.)