Suppose the life span of a light bulb is normally distributedwith mean 1000 hours and standard deviation 75 hours. (a) Find the57th percentile of this distribution. (b) Find the probability thata random light bulb will last longer than 1100 hours. (c) Find theprobability that the life span of a light bulb will be more than3.14 standard deviations away from the mean. (d) Suppose you take asample of 15 light bulbs and measure the average life span.Carefully justify whether the Central Limit Theorem applies, and ifit does, find the probability that the average life span is between950 and 1025 hours.
