A manufacturer of automobile batteries claims that the distribution of the life of its best battery has a mean of 54 months and a standard deviation of 6 months. Suppose a consumer group decides to check the claim by purchasing a sample of 50 of these batteries and subjecting them to tests that determine battery life.
(a) Assuming the manufacturer's claim is true, describe the sampling distribution of the mean lifetime of a sample of 50 batteries.
(b) Assuming the manufacturer's claim is true, what is the probability the consumer group's sample has a mean life of 52 or fewer months?
(c) What would your results be if the consumer group used a sample of 35 batteries instead of 50? Explain your results.