Question

A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 25 and a standard deviation of 8. The administrators decide to test the new program in one school of 200 students. What is the standard deviation of the comparison distribution

Answer 1

Answer:

The standard deviation of the comparison distribution is 0.5657.

Step-by-step explanation:

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

In this question:

Standard deviation of the population is 8, sample of 200. So

$s = \frac{8}{\sqrt{200}} = 0.5657$

The standard deviation of the comparison distribution is 0.5657.