The charge life of a certain lithium-ion battery for camcorders is normally distributed, with a mean of 90 minutes and a standard deviation of 35 minutes.

(A) What is the probability that a randomly selected battery of this type lasts more than 100 minutes on a single charge? Is this result unusual?

B) Describe the sampling distribution of x (is it normal?) and the sample means charge life for a random sample of 10 such batteries (x).

(C) What is the probability that a random sample of 10 such batteries has a mean charge life of more than 100 minutes? Is this result unusual?

D) What is the probability that a random sample of 25 such batteries has a mean charge life of more than 100 minutes?

E) Explain what causes the probabilities in parts (c) and (d) to be different.