Question

A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the percentage of bulbs that can be expected to last the period of time. Round to the nearest hundredth, if necessary.

Between 540 hours and 780 hours

44.3%

34.2%

44.34%

34.34%

Answer 1

The percentage of bulbs that can be expected to last the period of time is 34.2%

Finding the percentage of bulbs that can be expected to last the period of time

From the question, we have the following parameters that can be used in our computation:

Mean = 500 hours

Standard deviation = 100 hours

Also, we have

Score = Between 540 hours and 780 hours

The standard score of these is calculated using

z = (Score - Mean)/SD

So, we have

z = (540 - 500)/100 and z = (780 - 500)/100

z = 0.4 and z = 2.8

The percentage is then calculated as

Percentage = P(0.4 < z < 2.8)

Using the z table of probabilities, we have

Percentage = 34.2%

Hence, the percentage is 34.2%