Let X represent the amount of time until the next student will arrive in the library parking lot at the university.If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes (i.e.the mean number of arrivals is 1/4 per minute),find the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot.
A)0.917915
B)0.670320
C)0.329680
D)0.082085

Question

Quizplus · Accepted Answer

We know that the mean arrival time is 4 minutes, so the rate parameter (lambda) of the exponential distribution is 1/4. We need to find P(X > 10). Using the exponential probability density function, we get:

P(X > 10) = e^(-lambda*10) = e^(-2.5) = 0.082085

Therefore, the correct answer is D.

Let X Represent the Amount of Time Until the Next