A company installs 5,000 light bulbs. the lifetimes of the lightbulbs 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 the indicated amount of time. between 500 hours and 675 hours

Question

Leonidas Sawyer

Mathematics

24 February, 02:22

A company installs 5,000 light bulbs. the lifetimes of the lightbulbs 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 the indicated amount of time. between 500 hours and 675 hours

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Brendon Nicholson · Answer 1

First, determine the z-score of 675.

z = (675 - 500) / 100 = 1.75

The z-score of 500 is,

z = 0.

Subtracting the z-scores will give us 1.75. This is equal to 0.9599.

= 0.9599 - 0.5 = 0.4599

Multiplying this to the given number of light bulbs,

n = 0.4599 x 5000 = 2299.5

Therefore, there is approximately 2300 light bulbs expected to last between 500 to 675 hours.