Just like any light bulb, projector bulbs have an expected operating time, calle

Question

Just like any light bulb, projector bulbs have an expected operating time, called lamp life. This value is expressed in hours and represents the number of hours before the lamp loses its brightness. The life of projector's lamp is normally distributed with a mean of 2000 hours and a standard deviation of 200 hours. What is the expected life of projector bulbs? What is the probability that a projector fails before 1800 hours? What is the probability that the projector fails between 1900 and 2100 hours? What is the probability that a projector will fail at least after operating 2400 hours? What's is the number of hours before which the project will fail with a probability of 67%?

Explanation / Answer

The params of normal distribution are given:

Mu = 2000

Stdev = 200

Here are the answers :

1. E(X) = Mean = 2000 hours
2. P(X<1800) = P(Z< 1800-2000 /200) = P(Z<-1) = .16
3. P(1900<X<2100) = P(-.5<Z<.5) = 2*(.6915-.5) = .383
4. P(X>=2400) = P(Z> 3) = 1-.9987 = .0013
5. P(X<s) = .67, Z = .44 for .67 cumulative probability. No. of hours = .44*200+2000 = 2088

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