A large manufacturing plant uses a certain brand of light bulbs that has a mean

Question

A large manufacturing plant uses a certain brand of light bulbs that has a mean time to failure (MTTF) of 3600
hours with a standard deviation of 160 hours. Good lighting in the plant is critical to safety, and the plant manager
determines that no more than 10% of the bulbs should fail while being used. He institutes a policy to replace all the lightbulbs simultaneously according to a set schedule, rather than to replace individual bulbs as they burn out. After how manyhours should all the bulbs be replaced such that no more than 10% of the bulbs will fail while being used? (You may assume that the variations in MTTF are random.)

Explanation / Answer

P(X>x) = P(Z>(x-3600)/150) = 0.1

So z = 1.28 (from normal table)

1.28 = (x - 3600)/150

So x = 3792 hours

So After 3792 hours, all the bulbs should be replaced.

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