Question

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

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.