The time (in years)until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5
Years or more.
A)0.770210
B)0.229790
C)0.506617
D)0.493383

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-x/\lambda}$, where $\lambda$ is the mean. Here, $\lambda = 3.4$ years, and we want $P(X > 5)$. Thus, $P(X > 5) = e^{-5/3.4} \approx 0.229790$.

The Time (In Years)until the First Critical-Part Failure for a Certain