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 a standard deviation of
0.05
inch. A random sample of
11
tennis balls is selected. Complete parts​ (a)through​ (d) below.
Question content area bottom
Part 1
a. What is the sampling distribution of the​ mean?
A.Because the population diameter of tennis balls isapproximately normally​ distributed, the sampling distributionof samples of size
11
will also be approximately normal.
B.Because the population diameter of tennis balls isapproximately normally​ distributed, the sampling distributionof samples of size
11
will be the uniform distribution.
C.Because the population diameter of tennis balls isapproximately normally​ distributed, the sampling distributionof samples of size
11
cannot be found.
D.Because the population diameter of tennis balls isapproximately normally​ distributed, the sampling distributionof samples of size
11
will not be approximately normal.
Part 2
b. What is the probability that the sample mean is less than
2.68
​inches?
​P(X<2.68​)=enter your response here
​(Round to four decimal places as​ needed.)
Part 3
c. What is the probability that the sample mean is between
2.69
and
2.73
​inches?
​P(2.69<X<2.73​)=enter your response here
​(Round to four decimal places as​ needed.)
Part 4
d. The probability is
68​%
that the sample mean will be between what two valuessymmetrically distributed around the population​ mean?Thelower bound is
enter your response here
inches. The upper bound is
enter your response here
inches.
​(Round to two decimal places as​ needed.)