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. Less than 690 hours

A. 97.06%

B. 47.14%

C. 97.1%

D. 97.2%

Answer 1

Using the public distribution table given at http://www.math.unb.ca/~knight/utility/NormTble.htm
And keeping in mind that \[Z = {{X - \mu} \over \sigma}\]
For X = 690, mu = 500, sigma = 100, you get Z = 1.9.

According to the table, for Z = 1.9 the area under the gaussian is 0.9713. That is your probability.
The exact value of 97.13% is not an option, so we will choose C as our closest guess.

Answer 2

Thank you.