Question

The life expectancy of a typical lightbulb is normally distributed with a mean of 2,100 hours and a standard deviation of 40 hours. What is the probability that a lightbulb will last between 1,965 and 2,165 hours?

Answer 1

`\mathbb P(1965<X<2165)=\mathbb P\left((1965-2100)/(40)<(X-2100)/(40)<(2165-2100)/(40)\right)=\mathbb P(-3.375<Z<1.625)\approx0.9476`