7. (10 pts) Suppose an atomic reactor has two independent cooling systems. The probability that cooling system A will fail is .002 and the probability that cooling system B will fail is .003. What is the probability that both systems will fail simultaneously? Your answer is 8. (10pts) What is the area under the normal curve between z--0.40and z-0.55? Your answer is 9. (10pts) The life of light bulbs is distributed normally. The standard deviation of the life time is 25 hours and the mean lifetime of a bulb is 600 hours. Find the probability of a bulb lasting for between 550 and 620 hours. 10. (10pts) Find the value of z such that 0.5 of the area lies between -z and z. Your answer is 2