The lifetime of a stereo component is exponentially distributed with mean 1,000 days.What is the probability that the lifetime exceeds 1,000 days?
A).6321
B).5000
C).3679
D)1.000

Question

Quizplus · Accepted Answer

The probability that the lifetime exceeds the mean of 1,000 days is given by the complement of the probability that the lifetime is less than or equal to 1,000 days, so P(X > 1000) = 1 - P(X <= 1000). Using the exponential distribution formula, we have P(X <= 1000) = 1 - e^(-1000/1000) = 1 - e^(-1) = 1 - 0.3679 = 0.6321. Therefore, P(X > 1000) = 0.3679, which is choice C.

The Lifetime of a Stereo Component Is Exponentially Distributed with Mean