Customers arrive at a caf according to a Poisson process at the rate of one every...
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Customers arrive at a café according to a Poisson process at the rate of one every three minutes. Each customer can choose to either sit in the café or have a takeaway. The takeaway option is chosen by 39% of customers. Whether a customer chooses to sit in or have a takeaway is assumed to be independent of the choices made by other customers. (a) Calculate the probability that exactly three customers arrive in a 15 minute period. (b) Calculate the probability that, in a 15 minute period, at least two customers who have their order as a takeaway arrive at the café. (c) Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the café. Customers arrive at a café according to a Poisson process at the rate of one every three minutes. Each customer can choose to either sit in the café or have a takeaway. The takeaway option is chosen by 39% of customers. Whether a customer chooses to sit in or have a takeaway is assumed to be independent of the choices made by other customers. (a) Calculate the probability that exactly three customers arrive in a 15 minute period. (b) Calculate the probability that, in a 15 minute period, at least two customers who have their order as a takeaway arrive at the café. (c) Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the café.
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Solutions a To calculate the probability of exactly three customers arriving at the cafe within a 15minute period we use a formula called the Poisson distribution This formula allows us to determine t... View the full answer
Related Book For
Management Accounting Information for Decision-Making and Strategy Execution
ISBN: 978-0137024971
6th Edition
Authors: Anthony A. Atkinson, Robert S. Kaplan, Ella Mae Matsumura, S. Mark Young
Posted Date:
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