Question

Scores on the Critical Reading portion of the SAT college entrance test in a recent year were roughly Normal with mean 496 and standard deviation 115. You choose an SRS of 100 students and average their SAT scores. If you do this many times, the standard deviation of the average scores you get will be close to

A. 115

B. 115 / square root of 100 = 1.15

C. 115 / square of 100 = 11.5

Answer 1

C. 115 / square of 100 = 11.5

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`

In this problem, we have that:

`\sigma = 115, n = 100`. So

`s = (115)/(√(100)) = 11.5`

So the correct answer is:

C. 115 / square of 100 = 11.5