Question

Hello, I am struggling with a statistics problem. The problem states:

The diameter of ping-pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 2.30 inches and a standard deviation of .04 inch. What is the probability that a randomly selected ping-pong ball will have a diameter...

1. Between 2.28 and 2.30 inches

2. Between 2.31 and 2.33 inches

Then if many random samples of 16 balls are selected:

4.3 What proportion of the sample means would be between 2.28 and 2.30 inches?

4.4 What proportion of the sample means would be between 2.31 and 2.33 inches

I calculated the answers for each of the questions to be

1.) .1915

4.3) .4772

2.) .1747

4.4) .1574

I am struggling with comparing the answers in 1 and 4.3 as well as 2 and 4.4. I thought that the as the value in the denominator of the z formula increases (n) the overall answer should be smaller. However, when comparing my answers I realized that this was not necessarily true. Are my answers wrong? If not, how do I successfully explain comparing these answers?

Answer 1