If the sampled population has a mean of 48 and standard deviation of 16,then the mean and the standard deviation for the sampling distribution of $\bar { X }$
For n = 16 are:
A)4 and 1.
B)12 and 4.
C)48 and 4.
D)48 and 1.
E)48 and 16.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample means (i.e., $\bar{X}$) is equal to the mean of the population ($\mu$). Therefore, the mean of the sampling distribution of $\bar{X}$ is also 48.

The standard deviation of the sampling distribution of the sample means is given by the formula: $\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation of the population and n is the sample size. Substituting the given values, we get:

$\sigma_{\bar{X}} = \frac{16}{\sqrt{16}} = 4$

Therefore, the answer is C, 48 and 4.

If the Sampled Population Has a Mean of 48 and Standard