The lifetimes of a certain electronic component are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.
a. For a random sample of 16 components, find the probability that the sample mean is more than 1,500 hours.
b. For a random sample of 16 components, the probability is 0.15 that the sample mean lifetime is more than how many hours?
c. For a random sample of 16 components, the probability is 0.10 that the sample standard deviation lifetime is more than how many hours?