1. Guide to Using Minitab For Basic Statistical Applications
To Accompany
Business Statistics: A Decision Making Approach, 6th Ed.
Chapter 5:
Using Probability and Discrete Probability Distributions By
Groebner, Shannon, Fry, & Smith
Prentice-Hall Publishing Company
Copyright, 2005

2. Chapter 5 Minitab Examples
Binomial Mean -
Catalog Sales
Binomial Standard Deviation
Poisson Distribution
Heritage Tile
More Examples

3. Chapter 5 Minitab Examples
Standard Normal
State Bank and Trust
Exponential Distribution
Haines Internet Services

4. Binomial Mean Catalog Sales
Issue:
People who order items from catalogs can return the items for a refund. Historical return rate for one catalog has been 11 percent. Is this rate still valid?
Objective:
Use Minitab to compute binomial probabilities based on a sample of 300 purchases.

5. Binomial Mean – Catalog Sales
Situation
Sample Size is n=300
p = .11
Mean = np = 300(.11) = 33
44 returns were observed
P(X > 44) = 1 – P(X < 43)
Find P(X < 43) = ?

6. Binomial Probabilities – EPA Standards
Select Calc – Probability Distributions - Binomial

7. Binomial Mean – Catalog Sales
Specify Cumulative probability, Number of trials, success probability, and the Input constant (= number of successes)

8. Binomial Mean – Catalog Sales
Binomial Probability – Now Take = .03

9. Binomial Distribution Catalog Sales
Issue:
People who order items from catalogs can return the items for a refund. Historical return rate for one catalog has been 11 percent. There will be variation from sample to sample.
Objective:
Use Minitab to generate the binomial distribution and histogram to visually see spread in the distribution of possible results.

10. Binomial Distribution – Catalog Sales
Situation
Sample Size is n=300
p = .11
Mean = np = 300(.11) = 33
Standard Deviation =

11. Binomial Distribution – Catalog Sales
Select Calc – then select Probability Distribution – then Binomial

12. Binomial Standard Deviation – Catalog Sales
Binomial based on n=300 trials and p = Click OK.
Select Cumulative probability and enter the number of successes.

13. Binomial Distribution – Catalog Sales
Cumulative Probability P(x < 43) = P(x < 44)

14. Poisson Distribution Heritage Title Issue:
The distribution for the number of defects per tile made by Heritage Tile is Poisson distributed with a mean of 3 defects per tile. The manager is worried about the high variability
Objective:
Use Minitab to generate the Poisson distribution and histogram to visually see spread in the distribution of possible defects.

15. Poisson Standard Deviation – Heritage Tile
Select Calc – then select Probability Distributions – then Poisson
Create Number column (0 – 10)

16. Poisson Standard Deviation – Heritage Tile
Mean = 3.0
Select Probability and the Input column. Enter the Number column and storage column

17. Poisson Standard Deviation – Heritage Tile
To construct the histogram – see the process outlined in the Capital Credit Union tutorial in Chapter 2.

18. Standard Normal State Bank and Trust
Issue:
State bank managers have studied the time customers spend at the bank on business. They plan to offer a gift certificate to any customer who is required to spend over 30 minutes on bank business.
Objective:
Use Minitab to analyze to create histogram and determine the probability that a certificate will be given to any customer. The data file is State Bank.mtw.

19. Standard Normal – State Bank and Trust
Open Data File: State Bank.mtw

20. Create Cutpoint Column

21. Standard Normal – State Bank and Trust
Select Graph - Histogram

22. Standard Normal – State Bank and Trust
Define variable for analysis – Set Display to Bar – Click on Options

23. Standard Normal – State Bank and Trust
Select CutPoint as Type of Interval and insert Cutpoints column

24. Standard Normal – State Bank and Trust
Specify Color of Histogram bars, etc.
Check Edit Attributes

25. Standard Normal – State Bank and Trust
Use Annotate to set titles, etc.

26. Standard Normal – State Bank and Trust
Completed Histogram – next determine probability of a customer waiting over 30 minutes

27. Standard Normal – State Bank and Trust
Select Stat – Basic Statistics – Display Descriptive Statistics

28. Standard Normal – State Bank and Trust
Specify variable for analysis

29. Standard Normal – State Bank and Trust
Mean and Standard Deviation

30. Standard Normal – State Bank and Trust
Select Calc – Probability Distribution - Normal

31. Standard Normal – State Bank and Trust
Set to Cumulative Probability – Specify Mean and Standard Deviation and the input constant(x = 30 here)

32. Standard Normal – State Bank and Trust
P(X <30) = .9024
Then P (x > 30) = = .0976

33. Exponential Distribution Haines Internet Services
Issue:
The time between connect attempts averages two minutes and the distribution of time between attempts is assumed to be exponential.
Objective:
Use Minitab to compute the probability that that the time between connect attempts will be less or equal to 45 seconds.

34. Exponential Distribution – Haines Internet Services
Use Calc – Probability Distributions - Exponential

35. Exponential Distribution – Haines Internet Services
Check Cumulative – Specify Mean = 120 seconds and define input constant (= 45 here).

36. Exponential Distribution – Haines Internet Services
Exponential Distribution Probability Result
P(X < .45 seconds) = .3127