A manufacturing plant uses light bulbs whose life spans are normally distributed, with mean and standard deviation equal to 600 and 40 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.)

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FelisFelis FelisFelis · Answer 1 · 2019-11-22T12:42:03+01:00

Answer:

The bulbs be replaced after 517.85 hours, in order to maintain no more than 2% of the bulbs to burn out between replacement periods.

Step-by-step explanation:

Consider the provided information.

We need to find out the periods of replacement if we wish no more than 2% of the bulbs to burn out between replacement periods.

By using standard normal table find the critical value.

Corresponding critical value to the left tail is -2.0537

The value of μ=600 and σ=40.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substitute the respective values as shown:

[tex]-2.0537=\frac{x-600}{40}[/tex]

[tex]x-600=-82.148[/tex]

[tex]x=517.852[/tex]

Hence, the bulbs be replaced after 517.85 hours, in order to maintain no more than 2% of the bulbs to burn out between replacement periods.