Question

Customers arrive at a local ATM at an average rate of 15 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames.

​a) What is the probability that the next customer will arrive within the next 5 ​minutes?

​b) What is the probability that the next customer will arrive in more than 8 ​minutes?

​c) What is the probability that the next customer will arrive between 9 and 14 ​minutes?

Answer 1

Mean rate = 15 per hour = 60/15 = 4 per minute

a) P(X < 5) = 1 - e^-5/4 = 0.7135

b) P(X > 8) = e^-8/4 = 0.1353

c) P(9 < X < 14) = e^-9/4 - e^-14/4 = 0.0752