Question

The lifetimes of the light bulbs produced by Filip Company are normally distributed with a mean of 1,150 hours and a standard deviation of 175 hours.
What is the probability that a randomly chosen light bulb will have a lifetime of more than 1,000 hours?

Answer 1

Solution

Let lifetime of bulbs be x

X~N$(1150, {175} ^2)$

Pr(x>1000)=1-Pr(x<1000)

Obtaining the z-score of the above yields :

$\Phi ({1000-1150 \over 175}) = \Phi (-0.85714)$

Which follows x~N(0,1)

We can thus obtain the probability from statical tables.

$\Phi (-0.85714) =0.1957$

$1-\Phi (-0.85714)=0.8043$

Ans : 0.8043