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 less than 1 year.
A) 0.033373
B) 0.966627
C) 0.254811
D) 0.745189

Question

Quizplus · Accepted Answer

The exponential distribution with mean 3.4 years has a rate parameter λ = 1/3.4. The probability that the time until failure is less than 1 year is given by P(X < 1) = 1 - e^(-λ*1) = 1 - e^(-1/3.4), which is approximately 0.254811.

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