Question

Suppose that the scores of golfers in one round on the PGA tour has an average of 71.1 and standard deviation of 4.24.

According to the Central Limit Theorem, what happens to the histogram of averages as n increases?

a. The histogram will begin to look more like the original distribution.
b. Increasing n will not affect the histogram of averages.
c. The histogram will begin to look less like the normal curve.
d. It depends on the mean and standard deviation.
e. The histogram will begin to look more like the normal curve

Answer 1

e. The histogram will begin to look more like the normal curve

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`

According to the Central Limit Theorem, what happens to the histogram of averages as n increases?

The distribution is going to be approximately normal, which means that the histogram will look more like the normal curve.

So the correct answer is:

e. The histogram will begin to look more like the normal curve