The United States Golf Association (USGA) tests all new brands of golf balls to

Question

The United States Golf Association (USGA) tests all new brands of golf balls to assure that they meet USGA specifications. One of the tests is intended to measure the average distance traveled when the ball is hit by a machine called “Iron Byron”, a name inspired by the swing of the famous golfer Byron Nelson. The USGA proceeded to test with the Iron Byron machine over 250 golf balls of a new type called Ballistic, recording the distance travelled of each one.

What distribution will the sample average of the distance travel follow?

The discrete distribution

The binomial distribution

The normal distribution

Explanation / Answer

It should follow a normal distribution according to the central limit theorem which states that in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

Here, also sample mean is a normalized sum also, therefore it will also follow a normal distribution

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