On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. What is the probability that the appliance will work at least six years without requiring repairs?
A) 0.7769
B) 0.3456
C) 0.6544
D) 0.2231

Question

Quizplus · Accepted Answer

Let X be the time between repairs, then X is exponentially distributed with a mean of Mu = 4 years. The probability that the appliance will work at least 6 years without requiring repairs can be expressed as:

P(X > 6) = e^(-6/Mu) = e^(-6/4) = 0.2231

Therefore, the answer is D.

On Average, a Certain Kind of Kitchen Appliance Requires Repairs