Answer to Question #168628 in Statistics and Probability for Joe

Question #168628

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)

1
Expert's answer
2021-03-05T00:53:05-0500

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

  1. Here to find ϕ\phi ((1130-1200)/50) = 0.08
  2. Here to find ϕ\phi ((1275-1200)/50) - ϕ\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 - ϕ\phi ((1130-1200)/50) = 0.92

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