Question

Jacqueline is the general manager for a business. One of Jacqueline's tasks is to assign extra projects to her employees. These extra projects are supposed to be assigned following a particular order. The extra projects result in additional pay, so the employees are concerned that the extra projects are assigned following the proper procedure. Errors do happen though. Jacqueline makes an error once every 69 tasks that she assigns.

If Jacqueline were to assign 10 tasks, what is the probability that she would make 3 or more mistakes?  (Round your answer to six decimal places.)

When Jacqueline was supposed to assign 10 tasks to Jennifer, she DID make 3 mistakes. Was Jennifer treated fairly?

• yes
• no

What conclusions could you make about the three mistakes? Make sure to explain your conclusion thoroughly.

Answer 1

Average number of errors made for every 69 tasks = 1

Average number of errors made for every 10 tasks = 10*(1/69) =

Let X = Number of errors made for every 10 tasks

Then X~Poisson(0.145)

Required probability = P(X>=3) = (e^(-0.145))*(0.145^x)/x! {where x = 3,4,5,6,........}

So, P(X>=3) = 0.00046

No, Jennifer was not treated fairly.

Since, the probability that Jaqueline will make 3 or more mistakes is very low. The probability that she will make exatly 3 mistakes is even much lower. This means that it is very highly unlikely that Jaqueline would make 3 mistakes. Hence, it can be concluded that Jennifer was not treated fairly.

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