Answer to Question #255051 in Statistics and Probability for Sha

Question

If the standard deviation of the population is 25 and the sample size is 16 then the standard deviation of sampling distribution i

Answer 1

Given,

$n=16\\\sigma=25$

Sampling distribution of $\bar X$

$$\bar X\sim N(\mu, \dfrac{\sigma}{\sqrt n})$$

Mean, $\mu = \mu_{\bar X}$

Standard deviation of sampling distribution of mean-

$\sigma_{\bar X}=\dfrac{\sigma}{\sqrt n}=\dfrac{25}{\sqrt{16}}=\dfrac{25}{4}=6.25$

Hence, the standard deviation of sampling distribution $\boxed{\sigma_{\bar X}=6.25}$