Answer to Question #168628 in Statistics and Probability for Joe

Question

A manufacturer of light bulbs produces 100 Watt(W) bulbs that have lifetimes, L 

hours, which are normally distributed with mean 1200 hours and standard deviation 

50 hours. What is the probability that a randomly selected 100W bulb has a lifetime,

(a) Less than 1130 hours. (2)

(b) Between 1175 and 1275 hours? (2)

A room is fitted with three new 100W bulbs.

(c) What is the probability that I do not need to replace a bulb in the next 1130 hours?

(3)

Answer 1

In all points we need to use the cumulative distribution function (CDF) of the standard normal distribution, usually denoted with the capital Greek letter $\phi$ .

1. Here to find $\phi$ ((1130-1200)/50) = 0.08
2. Here to find $\phi$ ((1275-1200)/50) - $\phi$ ((1175-1200)/50) = 0.62
3. Here to find the probability that the lifetime will be more or equal than 1130. It's 1 - $\phi$ ((1130-1200)/50) = 0.92