A very large logging operation has serious problems keeping their skidders operating properly.The equipment fails at the rate of 3 breakdowns every 48 hours.Assume that x is time between breakdowns and is exponentially distributed.The probability of a single breakdown within 24 hours is:
A)0.0498
B)0.7769
C)0.2231
D)0.9502

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X \leq x) = 1 - e^{-\lambda x}$, where $\lambda$ is the rate of occurrence. Given 3 breakdowns every 48 hours, the rate $\lambda = 3 / 48 = 1/16$ breakdowns per hour. For a 24-hour period, $x = 24$, so $P(X \leq 24) = 1 - e^{-(1/16) * 24} = 1 - e^{-1.5} \approx 0.7769$.

A Very Large Logging Operation Has Serious Problems Keeping Their