Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours.

a. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 hours?

b. What is the probability that 16 randomly sampled batteries from the population will have a sample mean life of between 70 and 80 hours?

c. If the manufacturer of the battery is able to reduce the standard deviation of battery life from 10 to 9 hours, what would be the probability that 16 batteries randomly sampled from the population will have a sample mean life of between 70 and 80 hours?