Question

Not sure where to start and how to work this one. I tried but it is not multiple choice. Business Analysis 2372

A local credit union has hired a consulting firm to study the usage of one of its drive-up ATMs in order to see if another machine should be added to reduce customer wait time. The activity between 5 p.m. and 6 p.m. on weekdays is of particular interest. The consulting firm will record the number of customers that arrive in that one-hour time span each day. If more than 10 customers arrive, the consultants will record that day as "Busy" and perform further analysis on such days.

Assume that the customer arrival process between 5 p.m. and 6 p.m. on weekdays is reasonably modeled as Poisson with a mean of 7.8 arrivals per hour. What is the probability that any given weekday will be marked as "Busy," to three decimal places? Hint: I strongly recommend you use Excel's POISSON function; it will save you a lot of calculations!

Answer 1

Poisson's Distribution Formula:
P(X = x) = (e^-λ) (λ^x) / x!

Here, lambda = 7.8

we need to find P(x> 10)

P(x> 10) = 1 - P(x< 10)
= 1 - (P(x=0) + P(x=1) + P(x=2) +...... + (x =9))
= 1- e^-7.8*7.8^0/0! - e^-7.8*7.8^1/1! - ..... - e^-7.8*7.8^9/9!

= 1 - 0.8352
= 0.1648