Q. 7.27 - Elementary Statistics

Question

Why is obtaining the mean and standard deviation of $\overline{x}$ a first step in approximating the sample distribution of the sample mean by a normal distribution?

Step-by-Step Solution

Answer

The normal distribution always depends upon two parameters the mean and the standard deviation for any given random variable. Hence, the mean and standard deviation of $\overline{x}$ are obtained first when approximating the sample distribution of the sample mean by a normal distribution.

Step 1. Given Information

The objective is to find the reason why obtaining the mean and standard deviation of $\overline{x}$ is a first step in approximating the sampling distribution of the sample mean by a normal distribution.

Step 2. Explanation

A variable is normally distributed if its distribution has the shape of a normal curve and that a normal distribution is determined by the mean and standard deviation. 

Hence a first step in learning how to approximate the sampling distribution of the sample mean by a normal distribution is to obtain the mean and standard deviation of the sample mean, that is, of the variable $\overline{x}$.