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What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?

What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?

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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part 3 4

The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5-minute period,

  1. Find the expected value and standard deviation.
  2. What is the probability that 2 customers will arrive in a 5-minute period?
  3. What is the probability that no more than 2 customers will arrive in a 5-minute period?
  4. What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?
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