Lifetimes of a certain brand of light bulb have a mean and standard deviation of 100 hours. Suppose that your company owns a warehouse that contains 50 of these bulbs. (a) Using the Central Limit Theorem, what is the approximate distribution of sample average lifetime for the bulbs in the warehouse? (b) What is the probability that the average lifetime exceeds 120 hours? (c) Explain why you cannot use the CLT to determine the probability that a single light bulb lasts over 120 hours. (d) Could you use the CLT to approximate the distribution of the total lifetime of these bulbs?