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

Let X be a random variable representing the number of hours a bulb is expected to last.
P(X < 690) = P(z < (690 - 500)/100) = P(z < 190/100) = P(z < 1.9) = 0.97128 = 97.1%