An electronics repair shop has determined that the time between failures for a particular electronic component part is exponentially distributed with a mean time between failures of 200 hours. Based on this information, the probability that a part will fail in the first 20 hours is approximately 0.095.

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(T \leq t) = 1 - e^{-\lambda t}$, where $\lambda = \frac{1}{\text{mean time between failures}}$. For a mean time of 200 hours, $\lambda = \frac{1}{200}$. Plugging in $t = 20$ hours, we get $P(T \leq 20) = 1 - e^{-\frac{20}{200}} \approx 0.095$, which matches the given probability.

An Electronics Repair Shop Has Determined That the Time Between