DLP projectors are used in the majority of cinema projection systems and require a special light bulb to display a picture. Assume that the average life of a DLP bulb is 2,000 hours and that this failure time follows the exponential distribution. What is the probability that a randomly selected bulb will last less than 1,800 hours?

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}} = \frac{1}{2000}$. For $x = 1800$, $P(X < 1800) = 1 - e^{-\frac{1800}{2000}} = 1 - e^{-0.9} \approx 0.7774$.

DLP Projectors Are Used in the Majority of Cinema Projection