Question

A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing ​(Simplify your​ answer.) nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

Complete Question

A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26

Answer:

The mean of sampling distribution of the sample mean ( $\= x$) is $\mu_{\= x } = 77$

The standard deviation of sampling distribution of the sample mean ( $\= x$) is  

    $\sigma _{\= x} = 2.746$

Step-by-step explanation:

From the question we are told that

    The population mean is  $\mu = 77$

     The  standard deviation is  $\sigma = 14$

     The sample size is  $n = 26$

     

Generally the standard deviation of sampling distribution of the sample mean ( $\= x$) is  mathematically represented as

           $\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }$

substituting values  

          $\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }$

          $\sigma _{\= x} = 2.746$

Generally the mean of sampling distribution of the sample mean ( $\= x$) is  equivalent to the population mean i.e  

      $\mu_{\= x } = \mu$

      $\mu_{\= x } = 77$