Let X represent the amount of time it takes a student to park in the car park at the university.If we know that the distribution of parking times can be modelled 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 car park.
A) 0.329680
B) 0.670320
C) 0.917915
D) 0.082085

Question

Quizplus · Accepted Answer

We know that the mean of the exponential distribution is 4 minutes, which means that the rate parameter λ is equal to 1/4.

We can use the cumulative distribution function (CDF) of the exponential distribution to find the probability that a randomly selected student will take more than 10 minutes to park:

P(X > 10) = 1 - P(X ≤ 10)
            = 1 - F(10)
where F(x) is the CDF of the exponential distribution with rate parameter λ = 1/4:

F(x) = 1 - e^(-λx)
       = 1 - e^(-x/4)

Substituting x = 10, we get:

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

Therefore, the answer is D: 0.082085.

Let X Represent the Amount of Time It Takes a Student