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?