Customers arrive at a carwash with on average once every 20 minutes. It seems likely that customer arrivals follow an exponential distribution. In a simulation, the random number 0.1398 is generated. How long it will be until the next simulated arrival occurs?
A) 49.35 minutes
B) 39.35 minutes
C) 29.35 minutes
D) 19.35 minutes
E) 9.35 minutes

Question

Quizplus · Accepted Answer

The parameter of the exponential distribution is λ=1/20=0.05 (since the average arrival rate is once every 20 minutes). 
The random number generated from exponential distribution is given by the inverse transform method:
X = -ln(U)/λ
where U is the random number generated, and ln() is the natural logarithm function. 
Substituting the values given, we get:
X = -ln(0.1398)/0.05 = 39.35 
Therefore, the time until the next simulated arrival occurs is 39.35 minutes, which corresponds to option B.

Customers Arrive at a Carwash with on Average Once Every