The life expectancy of a typical lightbulb is normally distributed with a mean of 3,000 hours and a standard deviation of 38 hours. What is the probability that a lightbulb will last between 2,975 and 3,050 hours?

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Mathematics

Shiloh Rios

3 October, 06:18

The life expectancy of a typical lightbulb is normally distributed with a mean of 3,000 hours and a standard deviation of 38 hours. What is the probability that a lightbulb will last between 2,975 and 3,050 hours?

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Nigel Curry · Answer 1

You'll have to work out the area under the normal curve that maps to the range 2975-3050. So we have to scale the numbers to the world of the standard normal curve.

Step 1: subtract the mean, so that 0 is our mean. This means the range changes to - 25 ... + 50. (can you see that I subtracted 3000?)

Step 2: Divide by the standard deviation 38, so that the new sd becomes 1.

This means our range becomes - 0.66 to 1.32.

Now we have values that we can lookup in the standard normal table. This has to happen in two steps. First we lookup the probability for Z < 1.32, then we subtract the probability for Z<-0.66.

0.9066 - 0.2546 = 0.652 or 65.2%