High School

A population of values has a normal distribution with [tex]\mu=38.8[/tex] and [tex]\sigma=70.9[/tex]. You intend to draw a random sample of size [tex]n=246[/tex]. What is the mean of the distribution of sample means?

A. [tex]\mu_{\bar{x}} = 38.8[/tex]

B. [tex]\mu_{\bar{x}} = \frac{38.8}{\sqrt{246}}[/tex]

C. [tex]\mu_{\bar{x}} = \frac{70.9}{\sqrt{246}}[/tex]

D. [tex]\mu_{\bar{x}} = 70.9[/tex]

Answer :

Final answer:

The mean of the sample means distribution for a normal population is equal to the population mean, so the answer is a) μ¯x=38.8

Option a.

Explanation:

The question concerns the sampling distribution of the sample means. With a normally distributed population having a mean μ¯x=38.8 and standard deviation ( μ¯x of 70.9, when drawing a random sample of size n=246, the mean of the distribution of sample means is equal to the population mean, according to the Central Limit Theorem. Therefore, the correct option would be a)a) μ¯x=38.8

Option a.

Other Questions