Dead battery? A car company has found that the lifetime of its batteries varies from car

QUESTION:

Dead battery? A car company has found that the lifetime of its batteries varies from car to car according to a Normal distribution with mean m = 48 months and standard deviation s = 8.2 months. The company installs a new brand of battery on an SRS of 8 cars. (a) If the new brand has the same lifetime distribution as the previous type of battery, describe the sampling distribution of the mean lifetime x . (b) The average life of the batteries on these 8 cars turns out to be x = 42.2 months. Find the probability that the sample mean lifetime is 42.2 months or less if the lifetime distribution is unchanged. What conclusion would you draw?