Question

A manufacturing plant uses light bulbs whose life spans are normally distributed, with mean and standard deviation equal to 500 and 50 hours, respectively. In order to minimize the number of bulbs that burn out during operating hours, all the bulbs are replaced after a given period of operation. How often (in hr) should the bulbs be replaced if we wish no more than 2% of the bulbs to burn out between replacement periods? (Round your answer to two decimal places.)

Answer 1

602.50 hours

Explanation:

Given that a manufacturing plant uses light bulbs whose life spans are normally distributed, with mean and standard deviation equal to 500 and 50 hours,

It was decided to replace the bulbs so that no more than 2% of the bulbs to burn out between replacement periods

i.e. we have to construct 98% confidence interval right tailed to get this.

Z value is 2.05 for this (Upper tailed 0.98 probability)

Hence margin of error
`= 2.05 (std dev)\\=2.05(50)\\= 102.50`

The upper bound for this would be

`500+102.50 =602.50`

So to keep below 2% the bulbs to burn out it should be replaced before 602.50 hours.