Question

The mean and the standard deviation of a sampled population​ are, respectively, 113.9 and 32.1. Find the mean and standard deviation of the sampling distribution of the sample mean for samples of size n=64. Round your answers to one decimal place.

Answer 1

Answer: The mean and standard deviation of the sampling distribution of the sample mean for samples of size n=64 is

$113.9\text{ and }4.0$ respectively.

Step-by-step explanation:

Given : The mean of sampled population : $\mu = 113.9$

The standard deviation of sampled population : $\sigma = 32.1$

We know that the mean and standard deviation of the sampling distribution of the sample mean for samples of size n is given by :_

$\mu_s=\mu\\\\\sigma_s=\dfrac{\sigma}{\sqrt{n}}$

Now, the mean and standard deviation of the sampling distribution of the sample mean for samples of size n=64 will be :-

$\mu_s=113.9\\\\\sigma_s=\dfrac{32.1}{\sqrt{64}}=4.0125\approx4.0$