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 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

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  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

Quizplus · Accepted Answer

The probability that it will take more than 10 minutes for the next student to arrive can be calculated using the cumulative distribution function (CDF) of the exponential distribution with a mean of 4 minutes:
P(X > 10) = 1 - P(X ≤ 10) = 1 - (1 - e^(-10/4)) = 0.082085.
Therefore, the answer is D.

Let X Represent the Amount of Time Until the Next