Let X represent the amount of time it takes a student to park in the library parking lot at the university. If we know that the distribution of parking times can be modeled using an exponential distribution with a mean of 4 minutes, find the probability that it will take a randomly selected student more than 10 minutes to park in the library lot.
A) 0.670320
B) 0.082085
C) 0.329680
D) 0.917915

Question

Quizplus · Accepted Answer

We know that X follows an exponential distribution with a mean of 4 minutes. Therefore, the parameter lambda (the rate parameter) is equal to 1/4 (since the mean of an exponential distribution equals 1/lambda).

We want to find P(X > 10). Using the properties of the exponential distribution, we have:

P(X > 10) = e^(-lambda * 10)

Substituting lambda = 1/4, we get:

P(X > 10) = e^(-10/4) = 0.082085

Therefore, the answer is B.

Let X Represent the Amount of Time It Takes a Student