Question

Each year, a large warehouse uses thousands of fluorescent light bulbs that are burning 24 hours per day until they burn out and are replaced. The lifetime of the bulbs, X, is a normally distributed random variable with mean 620 hours and standard deviation 20 hours.

1. (a) If a light bulb is randomly selected, how likely its lifetime is less than 582 hours?

2. (b) The warehouse manager orders a shipment of 500 light bulbs each month. How

   many of the 500 bulbs are expected to have a lifetime that is less than 582 hours?

3. (c) The supplier of the light bulbs and the manager agree that any bulb whose lifetime

   is among the lowest 1% of all possible lifetimes will be replaced at no charge. What is the maximum lifetime a bulb can have and still be among the lowest 1% of all lifetimes?

Answer 1

a)

b) You can expect to have bulbs with lifetime that is less than 582 hours.

c) Let A be the value of the maximum lifetime a bulb can have and still be among the lowest 1% of all lifetimes.

critical Z value corresponding to probability 0.01 is -2.3263

hours