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

To acquire the exact form of the sampling distribution (normal distant) of the sample mean, we must first obtain the values of the sample mean's mean $\left(\mu \overline{x}\right)$and standard deviation $\left(\sigma \overline{x}\right)$.

Step 1: Given Information

We have To find The reason is obtaining the mean and standard deviation of $\overline{x}$ a First step in approximating the sampling distribution of the sample mean by a normal distribution.

Step 2: Explanation

Means $\left(\mu \right)$ and standard deviation $\left(\sigma \right)$ are the parameters of the normal distribution. The values of these parameters $\mu \& \sigma$are required to establish the exact form of the normal distortion.

To acquire the exact form of the sampling distribution (normal distant) of the sample mean, we must first obtain the values of the sample mean's mean $\left(\mu \overline{x}\right)$ and standard deviation $\left(\sigma \overline{x}\right)$