Question

How would you write the distribution of the sample mean X-bar with sample size of 36 if the population is X~N(200, 6^2 )?

A. X-bar ~N(200,1^2)

B. X-bar ~N(6.67,6^2)

C. X-bar ~N(200, 0.6^2)

D. X-bar~ unknown distribution with mean of 200 and standard deviation of 4.

Answer 1

$\mu _{\bar{x}}=200$

$\sigma _{\bar{x}}=\frac{\sigma }{\sqrt{n}}=\frac{6}{\sqrt{36}}=1$

Therefore,

Option A) is correct.

$\bar{x}\sim N(\mu _{\bar{x}},\sigma _{\bar{x}})$