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

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

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

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.

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) = ?

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

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

Binomial Mean – Catalog Sales Binomial Probability – Now Take 1- .97 = .03

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.

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

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

Binomial Standard Deviation – Catalog Sales Binomial based on n=300 trials and p = .11. Click OK. Select Cumulative probability and enter the number of successes.

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

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.

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

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

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

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.

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

Create Cutpoint Column

Standard Normal – State Bank and Trust Select Graph - Histogram

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

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

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

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

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

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

Standard Normal – State Bank and Trust Specify variable for analysis

Standard Normal – State Bank and Trust Mean and Standard Deviation

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

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

Standard Normal – State Bank and Trust P(X <30) = .9024 Then P (x > 30) = 1 - .9024 = .0976

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.

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

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

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