A car company claims that the lifetime of its batteries varies from car to car according to a Normal distribution with mean μ = 48 months and standard deviation σ = 8.2 months. A consumer organization installs this type of battery in an SRS of 8 cars and calculates x¯ = 42.2 months. 

a. Find the probability that the sample mean lifetime is 42.2 months or less if the company’s claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average lifetime of its batteries?