Question

A certain type of golfball is tested by a robot that hits the ball with a consistent impact force. The distances this

type of ball travels in this test are normally distributed with a mean of 195 meters and a standard deviation of 5
meters. Suppose that quality control experts regularly collect random samples of 25 distance measurements and
calculate the sample mean distance in each sample. Assume that the measurements in each sample are
independent.
What will be the shape of the sampling distribution of the sample mean distance?

Answer 1

Answer: approximately normal

Explanation:

1/2 Thinking about population shape and sample size

When a population is normally distributed, the sampling distribution of the sample mean x will also be normal regardless of sample size.

Since the distribution of distances is normal, the sampling distribution of the sample mean distance will also be normal.

2/2 Answer

The sampling distribution of the sample mean distance will be approximately normal.