1. Suppose you are the owner of a face painting business at a football game, and

Question

1. Suppose you are the owner of a face painting business at a football game, and you hire 2 workers to paint faces. There are three spots for customers to sit for their faces to be painted, and if a customer sits in the third spot you as the owner will paint that customers face. If all seats are filled with customers having their faces painted, then all customers will wait in line until a spot opens up for their face to be painted. Face painting service times are exponentially distributed with mean 30 minutes, and the mean time between arrivals for customers is 20 minutes. Please assume that if all 3 servers are painting faces, no one is waiting in line, and a customer leaves the system from 1 of the 2 workers that is not the owner, then the person having their face painted by the owner will go to the empty seat by the now freed worker, and the owner will wait for the next customer to come to the system a. What proportion of time is the owner of the face painting business painting customer faces? Note: if you answer this question correctly, you will be able to find the exact proportion of time that the owner is painting faces. Suppose that you as the owner want to spend at least 90% of your time prepping the paints for your workers and other managerial type of tasks instead of painting faces. What would the maximum arrival rate of customers need to be in order for the owner to spend at most 10% of his/her time painting faces? Please show all your work and write the expression to determine the maximum arrival rate of customers that allows the owner to spend 90% of his/her time not painting faces.

Explanation / Answer

In probability sampling, every member of the population has a probability higher than zero of being selected for the sample. To achieve this probability, the sample is obtained randomly.

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