Question

The life of light bulbs is distributed normally. the standard deviation of the lifetime is 25 hours and the mean lifetime of a bulb is 590 hours. find the probability of a bulb lasting for at most 622 hours. round your answer to four decimal places.

Answer 1

The probability is 0.8997.

We will use a z-score to answer this question.  z-scores are given by the formula
$z=\frac{X-\mu}{\sigma}$

With our information, we have
$z=\frac{622-590}{25}=\frac{32}{25}=1.28$

Looking this up in a z-table (http://www.z-table.com) we see that the area to the left of this (everything less than, up to this value) is 0.8997.