P7. The Company Sony produces an electronic device operated by two AA batteries. The distribution of the batteries' lifetime is close to a normal distribution with a mean of 35 hours, and a standard deviation of 5.5 hours. As part of its regular quality check process, Sony randomly draws a sample of 25 batteries.

(a) What is the sampling distribution of the sample mean? (Justify your answer).

(b) What is the standard error of the sample mean?

(c) What is the proportion of the sample with an average lifetime greater than 36 hours?

(d) What is the proportion of the sample with an average lifetime greater than 34.5 hours?

(e) What is the proportion of the sample with an average lifetime between 34.5

hours and 36 hours?