Question

The lifetime of light bulbs produced by a company are normally distributed with mean 1500 hours and standard deviation of 125 hours.

a). What is the probability that a bulb will still be burning after 1250 hours?

b). What is the number of hours that is survived by 78.81% of the light bulbs?

Answer 1

a)  Probability that a bulb will still be burning after 1250 hours

P( X > 1250) = P( Z >  x - μ/ σ )

= P( Z > 1250 - 1500 / 125)

= P (Z > -2)

P( Z < 2) = 0.9772 ( using standard normal table)

b)

We have to calculate x such that

P( X > x) = 0.7881

That is

P( X < x) = 1 - 0.7881

P( Z < x -   / ) = 0.2119

From Z table.,z-score for the probability of 0.2119 is -0.80

x -   / = -0.80

x - 1500 / 125 = -0.80

x = 1400 hours

number of hours that is survived by 78.81% of the light bulbs is 1400 hours