The diameter of a brand of ping-pong balls is approximately normally distributed, with a mean of 1.32 inches and a standard deviation of 0.08 inch. A random sample of 4 ping-pong balls is selected. Complete parts (a) through (d). a. What is the sampling distribution of the mean? A. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 4 will also be approximately normal. B. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 4 can not be found. C. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 4 will not be approximately normal. D. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 4 will be the uniform distribution.

a) A. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 4 will also be approximately normal.

b)

And using a calculator, excel or the normal standard table we have that:

c)

And using a calculator, excel or the normal standard table we have that:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Part a

Let X the random variable that represent the diameter of a brand of ping pong of a population, and for this case we know the distribution for X is given by:

Where and

And we select a sample of size n =4 and we want to find the distribution for

Since the distribution for X is normal then the distribution for the sample mean is normal and given by:

So the best option for this case would be:

A. Because the population diameter of Ping-Pong balls is approximately normally distributed, the sampling distribution of samples of 4 will also be approximately normal.

Part b

We can use the z score given by:

And using a calculator, excel or the normal standard table we have that:

Part c

And using a calculator, excel or the normal standard table we have that:

cute

Step-by-step explanation: