A type of lightbulb is labeled as having an average lifetime

A type of lightbulb is labeled as having an average lifetime of 4000 hours. It’s reasonable to model the probability of failure of these bulbs by an exponential density function with mean of 4000 hours. What is the median lifetime of these lightbulbs? Give your answer rounded to two decimal places.

Solution

The median is given by:
P(Lmedian) = P(Lmedian) = 0.5
P(Lmedian) = e^(-median/4000) = 0.5
-median/4000 = ln(1/2)
median = 4000 ln 2 = 2772.58 hours