Question

The lifetime of a lightbulb follows a normal distribution with mean 1500 hours and standard deviation of 100 hours. a. What is the probability that a lightbulb will last at least 1400 hours? b. What is the probability that a light bulb burns out in fewer than 1600 hours? c. What is the probability that a light bulb burns out in fewer than 1600 hours given that it has lasted 1400 hours? d. A technology breakthrough has occurred for which manufacturers claim that the lifetime will increase by 10%. What are the mean and variance of this new distribution? e. Calculate the probability that one of these new lightbulbs burns out in fewer than 1600 hours.

Answer 1

Let X denote the lifetime of a lightbulb. Then

a)

Required probability =

b)

Required probability =

c)

Required probability =

d)

Let Y denote the lifetime of the new lightbulb. Then So, Mean = 1650 and Variance = 12100

e)

Required probability =