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a)What is the probability that more than 3 customers arrive in 10 minutes? b)What is the probability that the time until the fifth customer arrives is less than 15 minutes?

a)What is the probability that more than 3 customers arrive in 10 minutes? b)What is the probability that the time until the fifth customer arrives is less than 15 minutes?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 3 minutes.

a)What is the probability that more than 3 customers arrive in 10 minutes?

b)What is the probability that the time until the fifth customer arrives is less than 15 minutes?

Round answers to 4 decimal places.

Expert Solution
Step 1

From given data we have 

Mean=1λ=3⇒λ=13

Let X denote the number of customers arriving per 10 minutes. So, here X follows a Poisson distribution with λ=10×14=104.

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