FC Industries manufactures two models of lamps. Prizm has a lifetime that is normally distributed with: a mean of 8,000 hours and a standard deviation of 600 hours. EcoLight is a more energy efficient and expensive lamp. It has a lifetime that is normally distributed with a mean of 8,500 hours and a standard deviation of 400 hours. a) What proportion of FC Prizm lamps will last exactly 8000 hours? b) What is the probability that the mean lifetime of EcoLight lamps in a sample of 225 lamps will last more than 8,450 hours? c) Suppose you select 120 Prizm lamps and 100 EcoLight lamps. What is the probability that the mean lifetime of Prizm lamps will not exceed that of EcoLight lamps? d) Suppose FC has a defect rate of 8%, what is the probability that a sample of 20 lamps has a sample proportion of greater than 0.07