Please see the attached file.

Statistics, All Topics
Year 3
Answer on fast question from attachment numbers from section 4 of attachment
You are manager of bank and you want to make sure customers do not have an overly long wait for a customer representative (other than the ATM or deposit box which requires no employee interaction). You know historically for each customer there is a X% chance a customer will walk in and will need customer service. You are going to try various scenarios in order to analyze the situation. Each student will be assigned a scenario is slightly different. I will do the first scenario.

90% probability a customer will walk through the door needing customer service. What percent of the time would you expect exactly 10 customers out of ten will require customer service?

Answer

Let X be the number of customers needing customer service out 10.
Clearly X is binomial with p = 0.90 , n =10,

The probability density function is given by
, x = 0,1..... 10

We need P(X=10)
= 0.348678

Thus 34.8678% of time 10 customers out of ten will require customer service.