Question

The diameter of a brand of tennis balls is approximately normally? distributed, with a mean of 2.79 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. Complete parts? (a) through? (d) below. a.

What is the sampling distribution of the? mean?

A.Because the population diameter of tennis balls is approximately normally? distributed, the sampling distribution of samples of size 10 cannot be found.

B.Because the population diameter of tennis balls is approximately normally? distributed, the sampling distribution of samples of size 10 will not be approximately normal.

C.Because the population diameter of tennis balls is approximately normally? distributed, the sampling distribution of samples of size 10 will also be approximately normal.

D.Because the population diameter of tennis balls is approximately normally? distributed, the sampling distribution of samples of size 10 will be the uniform distribution.

b. What is the probability that the sample mean is less than 2.77 ?inches?
?P( X <2.77?)= ?(Round to four decimal places as? needed.)
c. What is the probability that the sample mean is between 2.78 and 2.80 ?inches?
?P(2.78<X<2.80?)=?(Round to four decimal places as? needed.)
d. The probability is 61?% that the sample mean will be between what two values symmetrically distributed around the population? mean?
The lower bound is ___ inches. The upper bound is ____ inches.
?(Round to two decimal places as? needed.)

Answer 1

a)Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal.

b)

c)

d) p= 0.61

Lower bound= 2.74702

Upper bound= 2.833298