Question

A consumer buys n light bulbs, each of which has a life time that has a mean of 800 hours and a standard deviation of 100 hours. A light bulb is replaced by another as soon as it burns out. Assuming independence of life times, find the smallest value of n so that the succession of light bulbs produces light bulbs for at least 10,000 hours with a probability of 0.9. Do you think it is necessary to know the probability distribution of the light bulbs? Explain.