6. A contractor for a large office building is considering buying a large quantity of high intensity light bulbs from a certain manufacturer. The manufacturer assures the contractor that the average life of the bulbs is 1000 hours with standard deviation 80 hours. The builder decides to buy bulbs from this manufacturer only if a random sample of 64 such bulbs yields an average life of at least 1010 hours. What is the probability of the contractor buying these bulbs from this manufacturer? (Set up the problem by hand. Use tables or technology to solve numerically. )