Identify the Distribution of the Sample Mean $\bar { x }$

Multiple Choice

Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximatelynormal and give its mean and standard deviation.
-Let $x$ represent the number that shows up when a balanced die is rolled. Then $\mathrm { x }$ is a random variable with a mean of $3.5$ and a standard deviation of 1.71. Let $\bar { x }$ denote the mean of the numbers obtained when the die is rolled 40 times. Determine the sampling distribution of $\bar { x }$ .

A) Normal, mean $= 3.5$ , standard deviation $= 0.04$
B) Normal, mean $= 3.5$ , standard deviation $= 0.27$
C) Approximately normal, mean $= 3.5$ , standard deviation $= 0.27$
D) Approximately normal, mean $= 3.5$ , standard deviation $= 1.71$