Question

The lifetime of a particular type of light bulb are approximately normally distributed with a mean of 1200 hours and a standard deviation of 140 hours. At what number of hours should the warranty lifetime be set so that only 2% of bulbs must be replaced under warranty?

Answer 1

Given $\mu =1200$ and $\sigma =140$

Z-score of below 2% is $Z=-2.054$

Let the required time be hours

$X=\mu +Z\sigma =1200+(-2.054)140=912$ hours