Question

In: Statistics and Probability

Chris is the general manager for a business. One of Chris's tasks is to assign extra...

Chris is the general manager for a business. One of Chris's tasks is to assign extra projects to his 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. Chris makes an error once every 78 tasks that he assigns. If Chris were to assign 10 tasks, what is the probability that he would make 3 or more mistakes? (Round your answer to six decimal places.)

When Chris was supposed to assign 10 tasks to Alejandra, he DID make 3 mistakes.

Was Alejandra treated fairly? yes or no

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

Solutions

Expert Solution

Answer:

Given that,

Chris is the general manager of a business. One of Chris's tasks is to assign extra projects to his 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. Chris makes an error once every 78 tasks that he assigns.

Let X be the number of errors Chris make

AS number of trials is finite(number of tasks assigned is 10) and each trial is independent of other, the probability of success (making an error) is constant,

X follow binomial with n=10 and p=1/78=0.0128

The probability mass function of X is,

If Chris were to assign 10 tasks, what is the probability that he would make 3 or more mistakes:

To find P(X 3):

=1- [0.8791+0.1139+0.0067]

=1-[0.9997]

=0.0003

The probability of making 3 or mistakes 0.0003, which is very small (less than 0.05),

No Chris was not treated fairly.

As probability of making 3 or more mistakes is very small.

orchestra answered 2 years ago
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