The mean lifetime of a certain type of lightbulb produced by a manufacturing company is 200 months with a standard deviation of 30 months. Such a lightbulb will be guaranteed for 150 months by the company. The company will replace the lightbulb when the lightbulb fails before the expiration of the guarantee. If the length of life of the lightbulb is assumed to be normally distributed, what is the probability that there is at least one repalcement of five independent lightbulbs under the guarantee.
P(failure) = P(z) where z = (150 - 200) / 30 = - 5/3 = -1.67 = 0.04746 (for one particular bulb randomly chosen).
P(no failure) = 0.95254
P(no failure of 5 bulbs) = 0.952545 = 0.78418
P(at least one failure, 5 bulbs) = 1- the above = 0.21582