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

Question

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 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? O A. 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. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 cannot be found 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 not be approximately normal b. What is the probability that the sample mean is less than 2.62 inches? PR

Explanation / Answer

Answer to the question is as follows:

a. We have been given the distribution is approx normal

So ,according to the CLT ( central limit theorm) even the sampling distribution should be normal

So, C. is correct

b. P(Xbar<2.62) =?

Lets normalize using the params given out in the question,

P(Z< (2.62-2.63)/(.03/sqrt(10))

= P(Z<-1.054)

= .1459

We have used the Z tables here, to take out the probability

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