It is assumed that the time between failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. Based on this information, what is the probability that a randomly selected part will fail in less than 10 hours?
A) about 0.18
B) about 0.82
C) about 0.20
D) about 0.002
E) about 0.33

Question

Quizplus · Accepted Answer

The exponential distribution formula for the probability of failure before a certain time t is given by $P(T < t) = 1 - e^{-\lambda t}$, where $\lambda = \frac{1}{\text{mean time between failures}}$. Given a mean of 50 hours, $\lambda = \frac{1}{50}$. For $t = 10$ hours, $P(T < 10) = 1 - e^{-\frac{10}{50}} = 1 - e^{-0.2} \approx 0.18$.

It Is Assumed That the Time Between Failures for an Electronic