Question

It is known that the lifetime of a certain type of light bulb is normally distributed with

a mean lifetime of 1,060 hours and a standard deviation of 125 hours. What is the

probability that a randomly selected light bulb will last between 1,000 and 1,100 hours?

Answer 1

Solution:

Given that,

   = 1060

= 125

p (1000 < x < 1100 )

= p ( 1000- 1060 / 125 ) < ( x -  /   ) < ( 1100- 1060 / 125)

= p (- 60 /125 < z < 40 /125 )

= p (- 0.48 < z < 0.32)

= p ( z < 0.32 ) - p ( z < - 0.48 )

Using z table

= 0.6255 - 0.3156

= 0.3099

Probability = 0.3099