SOLUTION: PLease help, I've posted multiple times but still haven't gotten an answer. A company installs 5,000 light bulbs. The lifetimes of the light bulbs are approximately normally distr

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Question 964329: PLease help, I've posted multiple times but still haven't gotten an answer.
A company installs 5,000 light bulbs. The lifetimes of the light bulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the approximate number of bulbs that can be expected to last between 290 hours and 540 hours.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you have 5000 light bulbs.
their average life is 500 hours with a standard deviation of 100 hours.
you want to know how many light bulbs are expected to last between 290 and 540 hours.

you need to find the z-score of 290 hours and 540 hours and then you need to find the area under the distribution curve between them and then you need to multiply that by 5000 to get your answer.

z-score = (actual score minus mean) / standard deviation.

z1 = (290 - 500) / 100 = -210/100 = -2.1

z2 = (540 - 500) / 100 = 40/100 = .4

from the z-score table, the area under tyhe distribution curve to the left of z1 is .0179 and to the left of z2 is .6554.

the area between is equal to .6554 - .0179 = .6375

.6375 * 5000 = 3187.5

that's the number of light bulbs that are expected to have a lifespan of between 290 and 540 hours.