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) 0.917915
B) 0.670320
C) 0.329680
D) 0.082085

Question

Quizplus · Accepted Answer

We know that X has an exponential distribution with a mean of 4 minutes. Therefore, the parameter λ of the distribution is λ = 1/4 (since the mean of an exponential distribution is equal to 1/λ).

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

P(X > 10) = 1 - P(X ≤ 10) = 1 - F(10)

where F(x) is the CDF of the exponential distribution:

F(x) = 1 - e^(-λx)

Plugging in λ = 1/4 and x = 10, we get:

P(X > 10) = 1 - F(10) = 1 - (1 - e^(-10/4)) ≈ 0.082

Therefore, the answer is D) 0.082085.

Let X Represent the Amount of Time It Takes a Student