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QUESTION

# Suppose you are the manager of a coffee shop with three servers, who each take an average of 1.7minutes to serve a customer.

Suppose you are the manager of a coffee shop with three servers, who each take an average of 1.7minutes to serve a customer. You are concerned about your service during peak hours, and areconsidering making an investment to improve service. During peak hours, you have 1.3 customers perminute arriving on average.You have two options to ensure faster service: (a) hire a fourth server at an annual cost of \$38,000, or(b) rent faster dispensing machines at an annual cost of \$25,000, which would reduce service time to1.25 minutes, on average.You decide to base your decision on the number of customers who arrive during the time you can servethem. You don’t want to have a more than 10% chance of more customers arriving than you can serve.For instance, with your current operation, you can serve three customers in 1.7 minutes, so you don’twant the chance of more than three customers within 1.7 minutes to be greater than 10%.What should you do – continue the current operation, hire a fourth server, or rent faster dispensing machines?

My personal question is:

Is this a poisson distribution? I tried it out, but probabilities like 0.17, 0.20 and something else. All of which are over 10%?