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) 0.229790
B) 0.506617
C) 0.770210
D) 0.493383

Question

Quizplus · Accepted Answer

The probability that the time until the first critical-part failure is 5 years or more is given by the cumulative distribution function of the exponential distribution:$$P(X \ge 5) = 1 - P(X < 5) = 1 - (1 - e^(-5/3.4)) = e^(-5/3.4) = 0.229790$$

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