Question

The life expectancy of a typical lightbulb is normally distributed with a mean of 2,000 hours and a standard deviation of 27 hours. What is the probability that a lightbulb will last between 1,975 and 2,050 hours?

Answer 1

Step 1:
normalize.
\(\mu\)=2000
\(\sigma\)=27
use \(Z=(x-\mu)/\sigma\) to find z1 and z2 for x1=1975 and x2=2050.
From the normal distribution curve, find the area between z1 and z2, which is also the probability that z lies between z1 and z2, or x lies between x1 and x2.