The diameter of a brand of Ping-Pong balls is approximately normally distributed

Question

The diameter of a brand of Ping-Pong balls is approximately normally distributed with a mean of 1.31 inches and a standard deviation of 0.08 inch. A random sample of 16 Ping-Pong balls is selected. Complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table Click here to view page 2 of the cumulative standardized normal distribution table a. What is the sampling distribution of the mean? OA Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 16 will not be approximately normal. OB. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 16 will also be approximately normal. OC. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 16 can not be found. b. What is the probability that the sample mean is less than 1.28 inches? P(X

Explanation / Answer

a.The sampling distribution of mean is also normal as B.The population diameter of ping pong ball is approximately normally distributed and the sampling distribution of samples of 16 will also be approximately normal.

b.The mean is 1.31 and standard deviation is: 0.08/sq rt16=0.02

For X bar=1.28, z=(x bar-mu)/sigma

=(1.28-1.31)/0.02

=-1.5

Thus,P(X bar<1.28)=P(z<-1.5)

=0.0668

c.For X bar=1.3, z=(1.3-1.31)/0.02=-0.5

P(1.28<X bar<1.3)

=P(X bar<1.3)-P(X bar<1.28)

=P(z<-0.5)-P(z<-1.5)

=0.3085-0.0668

=0.2417

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