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)0.254811
B)0.966627
C)0.033373
D)0.745189

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}}$. Here, the mean is 3.4 years, so $\lambda = \frac{1}{3.4}$. For $x = 1$ year, $P(X < 1) = 1 - e^{-\frac{1}{3.4}} \approx 0.254811$.

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