Question

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118. You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to (a) 118 (b) 118/100=1.18. (c) 118/V100 11.8

Answer 1

Answer:

(c) 118/V100 11.8

Step-by-step explanation:

We use the central limit theorem to solve this question.

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 $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\sigma = 118, n = 100$

So

$s = \frac{118}{\sqrt{100}} = 11.8$

So the correct answer is:

(c) 118/V100 11.8