The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft²) and a standard deviation of 2 ft². To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to be x¯ = 249.6 ft².

a. Find the probability that the sample mean area is 249.6 ft² or less if the manufacturer’s claim is true.

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