the car manufacturer samples six cars from its assembly line and tests them for mileage ratings.

a$.$ What is the distribution of the mean mpg for the sample?

b$.$ What is the probability that the mean mpg of the sample will be greater than $34mpg?$

c$.$ What is the probability that the mean mpg of the sample will be less than $32\mathrm{.}5mpg?$

a$.$ What is the distribution of the mean mpg for the sample? Select the correct choice below and fill in the answer boxes to complete your choice.

$($Type integers or decimals rounded to two decimal places as needed.$)$

A$.$ The sampling distribution of the mean follows a triangular distribution with the sample mean $mpg$ and the standard deviation of the sample mean mpg$.$

B$.$ The sampling distribution of the mean follows a uniform distribution with the sample mean mpg and the standard deviation of the sample mean mpg$.$

C$.$ The sampling distribution of the mean follows an exponential distribution with the sample mean mpg and the standard deviation of the sample mean mpg

D$.$ The sampling distribution of the mean follows a normal distribution with the sample mean mpg and the standard deviation of the sample mean mpg$.$