The waiting time, in minutes, to see a teller at a large bank follows an exponential distribution. If the proportion of all customers who wait more than 15 minutes is 0.01, what is the mean waiting time for all customers?

Question

Charlie Russell

Mathematics

1 February, 23:36

The waiting time, in minutes, to see a teller at a large bank follows an exponential distribution. If the proportion of all customers who wait more than 15 minutes is 0.01, what is the mean waiting time for all customers?

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Efrain · Answer 1

Answer: 0.00067 minutes

Step-by-step explanation: if the proportion of customers who wait more than 15 minutes is 0.01, then the time interval between each waiting customer 15/0.01 = 1500 minutes.

The distribution that defines this question is that of an exponential.

An exponential distribution is dependent on the fixed time rate at which the event is occurring (λ)

For this question of ours, λ = 1500 minutes.

The mean of an exponential distribution is given as

u = 1 / λ = 1/1500 = 0.00067 minutes.