The diameter of a brand of tennis balls is approximately normally? distributed,

Question

The diameter of a brand of tennis balls is approximately normally? distributed, with a mean of

2.55 inches and a standard deviation of 0.04

inch. A random sample of 11 tennis balls is selected.

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 will be the uniform distribution.

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

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

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

b. What is the probability that the sample mean is less than

2.54inches?

?P(X <2.542.54?)=

Explanation / Answer

a. What is the sampling distribution of the? mean?

sampling distribution of the sample mean is normal with mean=2.55 and sd=0.04/sqrt(11)=0.01206

OPTION C

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

b. What is the probability that the sample mean is less than

2.54inches?

?P(X <2.542?)

Z=x-mean/sd

=2.54-2.55/0.04/sqrt(11)

Z=-0.83

P(Z<=-0.83)

=1-P(Z<0.83)

=1-0.7967

=0.2033

ANSWER:0.2033

he probability that the sample mean is less than

2.54inches=0.2033

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