Question

A large manufacturing plant uses lightbulbs with lifetimes that are normally distributed with a mean of 1400 hours and a standard deviation of 70 hours. To minimize the number of bulbs that burn out during operating hours, all bulbs are replaced at once. How often should the bulbs be replaced so that no more than 1% burn out between replacement periods? (Round your answer to one decimal place.)

Answer 1

First, we need to find the probability P( z less than or equal to 0.01 or 1%)

Using the standard normal table, we get the value P(z less than or equal to 0.01 or 1%) = -2.32

now, we have the z value, mean value and the standard deviation.

Using the formula

setting the given values, we get

multiplying both sides by 70, we get

-2.32*70 = (x-1400)

-162.4 = x-1400

adding 1400 on both sides, this gives

1400 - 162.4 = x - 1400 + 1400

x = 1237.6 hours

So, we need to replace bulbs after 1237.6 hours