Question

The lifetime of a particular bulb is a random variable with an average of μ = 2000 hours and a standard deviation of σ = 200 hours.

(c) Calculate the probability that a bulb will last more than 2300 hours if it lasts longer than 2100 hours.
(d) Calculate the probability that a bulb will last less than 2150 hours if it has lasted more than 2050 hours.

Answer 1

Let X : Lifetime of a particular bulb

Suppose, X has normal distribution

Given mean = = 2000 and standard deviation = = 200

c) To find the probability that a bulb will last more than 2300 hours if it lasts longer than 2100 hours, i.e., P(2100<X<2300)

Using Central Limit Theorem,

.......................... from the z score table

Therefore, Probability that a bulb will last more than 2300 hours if it lasts longer than 2100 hours is 0.1498

d) To find the probability that a bulb will last less than 2150 hours if it has lasted more than 2050 hours, i.e., P(2050<X<2150).

.......................... from the z score table

Therefore, the probability that a bulb will last less than 2150 hours if it has lasted more than 2050 hours is 0.1747