Question

Scores on the Critical Reading Part of the SAT exam in a recent year were roughly Normal with mean 501 and standard deviation 112. you choose an SRS of 100 Students and average their SAT crigical reading scores.

if you do this many times, the mean of the average scores you get will be close to:

A) 112

B) 501/100 = 5.01

C) 501/ square root of 100 = 50.1

Answer 1

The mean of the average scores will be 501 and the standard deviation will be
`s = (112)/(√(100)) = 11.2`

Explanation:

Central Limit Theorem

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that

For the population, mean 501 and standard deviation 112.

SRS of 100.

So, by the Central Limit Theorem

The mean of the average scores will be 501 and the standard deviation will be
`s = (112)/(√(100)) = 11.2`