Introduction to Statistical Analysis for Managers: Data andStatistics

JEFF GILL

Center for Applied Statistics

Washington University, St. Louis

Olin School of BusinessEMBA Program, [1]

Case Study: Binomial Distribution

The accounting department is concerned about the integrity of a new online ordering system that

the company has put in place.

Due to the volume of ordering not every order can be checked by a human.

Any questionable orders will be tagged by software if it falls outside of specified parameters.

Tagged orders are checked by humans for errors.

A management consultant has suggested that 0.10 of those ordered tagged will have to be manually

adjusted, which may involve contacting the customer.

This suggests that there is a hiring/staffing issue that did not exist before.

Olin School of BusinessEMBA Program, [2]

Case Study: Binomial Distribution

Day 1 of the new auditing system N = 973 were tagged.

We know that p = 0.1.

What is the probability that exactly x = 100 orders will have to be manually adjusted?

We will use the binomial probability function:

f(x|N, p) =

(N

x

)px(1 p)Nx

=N !

x!(N x)!px(1 p)Nx

=973!

100!(973 100)!(0.1)100(0.9)973100

= 0.04

Olin School of BusinessEMBA Program, [3]

Case Study: Binomial Distribution, excel

Suppose our real question is not the probability of exactly 100 orders to be manually adjusted but

the probability of less than 100 orders since above that we will have to hire another adjuster.

Low-method: calculate p(0) + p(1) + p(2) + . . . + p(99) + p(100).

Fortunately excel takes care of this for us.

Olin School of BusinessEMBA Program, [4]

Case Study: Binomial Distribution, excel

On the menu bar, click on Insert. Select Function. A new window with a list of functions will

appear.

From the functions list, select Statistical. For function name, select Binomdist.

Enter the following arguments for Binomdist:

Number-s is the number of successes (x)

Trials is the number of trials (N)

Probability-s is the probability of success (p)

Cumulative is a logical value. Type true if you want a cumulative

probability (P[X = x]). Type true if you want the cumulative probability.

Click OK. The result will be printed on the cell where your cursor was last located.

p(x 100) = 0.6385.

Olin School of BusinessEMBA Program, [5]

Case Study: Poisson Distribution

Suppose at a large manufacturing plant there have been an average of 2.5 work-related injuries

per month for the last three years.

As Safety Manager you would like to calculate the probability of no injuries next month.

Use the Poisson distribution function:

p(x|) =xe

x!

=2.50e2.5

0!

=1(2.71828)2.5

1

= 0.0821.

Olin School of BusinessEMBA Program, [6]

Case Study: Hypergeometric Distribution

Suppose you are forming a team of n = 8 executives from different departments for a special

project.

There are N = 30 total, and r = 10 are from the finance department.

What is the probability that that the team will have x = 2 executives from the finance department?

Use the hypergeometric probability distribution:

f(x|N,n, r) =

(rx

)(Nrnx

)(Nn

)

=

(10

2

)(301082

)(

30

8

)

=

(10!

2!8!

) (20!

6!14!

)(

30!

8!22!

)= 0.298