Service times at a doctor's office take an average of 40 minutes. It seems likely that service times follow an exponential distribution. In a simulation, the random number 0.7588 is generated. How long it will be until the next simulated arrival occurs?
A) 1 minute
B) 6 minutes
C) 11 minutes
D) 16 minutes
E) 21 minutes

Question

Quizplus · Accepted Answer

If service times follow an exponential distribution with an average of 40 minutes, then the rate parameter λ can be calculated as 1/40. The time until the next arrival follows the same exponential distribution with the same rate parameter λ. Using the formula for the cumulative distribution function of the exponential distribution, we get:

P(X > x) = e^(-λx)

where X is the time until the next arrival.

Plugging in the given random number 0.7588, we can solve for x:

0.7588 = e^(-λx)
ln(0.7588) = -λx
x = -ln(0.7588) / λ
x = -ln(0.7588) * 40

Using a calculator, we can find that x is approximately 11 minutes. Therefore, the best choice is C) 11 minutes.

Service Times at a Doctor's Office Take an Average of 40