If arrivals occur at a mean rate of 3.6 events per hour,the exponential probability of waiting less than 0.5 hour for the next arrival is
A)0.7122
B)0.8105
C)0.8347
D)0.7809

Question

Quizplus · Accepted Answer

First, we need to calculate the rate parameter of the exponential distribution. The mean rate of arrival is given as 3.6 events per hour, which means the rate parameter is λ = 3.6.

The probability of waiting less than 0.5 hour for the next arrival can be calculated as follows:

P(X < 0.5) = 1 - e^(-λt)

where t is the waiting time, in this case, 0.5.

P(X < 0.5) = 1 - e^(-3.6*0.5) = 0.8347

Therefore, the correct answer is C, 0.8347.

If Arrivals Occur at a Mean Rate of 3