Our light bulb manufacturer wants to estimate how long
his new LED light bulbs will last. He takes a random sample of 40
such bulbs and determines that the sample mean is 45500 hours with
a standard deviation of 1200 hours.
(a) Determine a 96% confidence interval for the true
mean life of these bulbs.
(b) If we approximate the population mean life of these
bulbs by the sample mean, what is the maximum possible error we
would (with 96% confidence).
(c) If we want the error in (b) to be less than 150
hours, how large a sample must we take?