Objective 1: To simulate the rolling of a die 100 times and to build a probability distribution.

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1 Minitab Lab #2 Math 120 Nguyen 1 of 6 Objectives: 1) Simulate games of chance that have equally likely outcomes 2) Construct a binomial probability distribution and sketch a probability histogram 3) Calculate the probability of a normal random variable and find a score corresponding to an area. Note: In the following instructions underlined words indicate what information you type in. A. Steps to start the MINITAB program: IMPORTANT: Do the following command only once. Please be patient. It can take MiniTab awhile to load when everyone is starting Minitab at the same time. Click on: Start > All Programs > Minitab 14 For Windows > Minitab 14 B. Steps to open (or retrieve) a saved project: 1. Click on: File > Open Project In the Open Project window: a. Click on the down arrow in the Look-in: box and select the K: drive > NatrlSci folder > GNguyen b. Double click on Lab Two.MPJ 2. On the screen in the worksheet window you should see the following columns : Roll of Die Murders Probabilities Scores C. Steps to save your project: 1. Click on: File > Save Project As In the Save Project As window: a. In the Save in: box, select the H: drive b. In the File Name box type: Lab Two - your name c. Click on the Save button Objective 1: To simulate the rolling of a die 100 times and to build a probability distribution. The following Minitab command, Calc > Random Data > Integer generates random data from an integer distribution, which is a discrete uniform distribution that ranges from the minimum to the maximum integer value specified. Each integer in the range has equal probability. D. Steps to simulate the rolling of an eight-sided die 100 times 1. Click on: Calc > Random Data > Integer In the Integer Distribution window: a. Click in the Generate: box and enter: 100 b. Click in the Store in column(s): box. to make the column list appear in the box on the left c. Double click on C1 Roll of Die in the box on the left to pump this variable to the Store in column(s): box d. Click in the Minimum value: box and enter: 1 e. Click in the Maximum value: box and enter: 8 f. Click on the OK button

2 Minitab Lab #2 Math 120 Nguyen 2 of 6 You should see a list of numbers appear in the Roll of Die column. E. Save your project: Click on the save file icon Now, you will build the probability distribution. F. Steps to obtain the counts and relative frequencies in the simulation 1. Click on: Stat > Tables > Tally Individual Variables In the Tally Individual Variables window: a. Double click on C1 Roll of Die in the box on the left to pump this variable to the Variables: box b. Click in the box to the left of Counts to uncheck this box. c. Click in the box to the left of Percents to make a check appear in this box. d. Click on the OK button Note: In the Session window your table will be different than the one shown on the right because each list is randomly generated. Roll of Die Percent G. Save your project: Click on the save file icon Objective 2: To construct a binomial probability distribution and a probability bar chart According to Crime in the U.S, 1998, 65% of murders are committed with a firearm. Suppose 10 murders are randomly selected. Let X represent the number of murders committed with a firearm. Here X is a random variable that has a binomial probability distribution. H. Steps to obtain a binomial probability distribution 1. Click on: Calc > Probability Distributions > Binomial In the Binomial Distribution window: a. Click on the button to the left of Probability b. Click in the Number of trials: box and enter: 10 c. Click in the Probability of success: box and enter: 0.65 d. Click on the button to the left of Input column e. Click in the box to the right of Input column to make the column list appear in the box on the left f. Double click on C3 Murders in the box on the left to pump this variable to the Input columns box

3 Minitab Lab #2 Math 120 Nguyen 3 of 6 g. Click in the Optional storage box that is under the Input columns box. h. Double click on C4 Probabilities in the box on the left to pump this variable to the Optional storage box i. Click on the OK button You should see a list of numbers appear in the Probabilities column. 2. To display the binomial probability distribution in the session window Click on: Data > Display Data In the Display Data window: a. Double click on C3 Murders in the box on the left to pump this variable to the Columns, constants, and matrices to display: box b. Double click on C4 Probabilities in the box on the left to pump this variable to the Columns, constants, and matrices to display: box c. Click on the OK button In the Session window, you should see a table of Data Display. I. Save your project: Click on the save file icon J. Steps to draw a probability bar chart 1. Click on: Graph > Bar Chart In the Bar Charts window: a. Click on the down arrow in the Bars represent pull down menu and select Values from a table b. Under One column of values click on Simple c. Click on the OK button

4 Minitab Lab #2 Math 120 Nguyen 4 of 6 2. In the Bar Chart Values from a table, One Column of values, Simple window: a. Click in the box under Graph variables b. Double click on C4 Probabilities in the box on the left to pump this variable to the Graph variables box c. Click in the box under Categorical variable d. Double click on C3 Murders in the box on the left to pump this variable to the Categorical variable box e. Click on the OK button You should see the probability bar chart displayed to the right. To have a Histogram, the bars need to touch. 3. Steps to make the bars touch in the bar chart Move the cursor to lie on top on any number that is below the x-axis until you see the message: X Scale. Then double click to edit the X scale In the Edit Scale window: a. Click on the Scale tab b. Click in the check box to the left of Gap between clusters to uncheck this box. This turns off the Auto (or default) feature. c. Click in the box to the right of Gap between clusters and change this value to 0 d. Click on the OK button You should see the probability histogram displayed to the right. 4. To insert your name on the graph and print it: a. Right-click on the title, select Add select Title type in your name following the title b. Print the Graph: The graph bar should be blue; if it is not, highlight the graph (Click on the graph bar, the bar turns blue) then to the menu File>Print graph

5 Minitab Lab #2 Math 120 Nguyen 5 of 6 K. Save your project: Click on the save file icon Objective 3: Calculate the probabilities of a normal random variable and find a score corresponding to an area. Calculate an area given a z-value: Minitab is like the z-tables in the text, only the area to the left of a z-value is given. L. Steps to calculate P(z < 1.56) 1. Click on: Calc > Probability Distributions > Normal In the Normal Distribution window: a. Click on the button to the left of Cumulative probability b. Click in the box to the right of Mean: and enter: 0 c. Click in the box to the right of Standard Deviation: and enter: 1 d. Click on the button to the left of Input constant: e. Click in the box to the right of Input constant: and enter: 1.56 f. Click on the OK button In the Session window, you should see the result under Cumulative Distribution Function M. Save your project: Click on the save file icon Find a z-score given an area: Minitab is like the TI-83+, the area entered must be to the left of a z-value. N. Steps to find a z-value with an area of 0.75 to its left 1. Click on: Calc > Probability Distributions > Normal In the Normal Distribution window: a. Click on the button to the left of Inverse cumulative probability b. Click in the box to the right of Mean: and enter: 0 c. Click in the box to the right of Standard Deviation: and enter: 1 d. Click on the button to the left of Input constant: e. Click in the box to the right of Input constant: and enter: 0.75 f. Click on the OK button

6 Minitab Lab #2 Math 120 Nguyen 6 of 6 In the Session window, you should see the result under Inverse Cumulative Distribution Function O. Save your project: Click on the save file icon P. Print the Session window. Make sure to type Your Name on the Session window screen. The session window bar should be blue; if it is not, highlight the session window (click on the session window bar, the bar turns blue), then go to the menu File>Print Session window. Q. Type a TITLE PAGE (using MS Word) for the lab, include Lab Title, Date, Your Name, and Analysis. Print this page out. Your Analysis should include your work (in either pen or pencil) to get the answers to the following questions: 1) Based on your probability distribution obtained in part F, what is the probability of getting an even face? (Your answer is likely to be different from everyone s answers.) 2) Based on your binomial probability distribution obtained in part H: What is P X 5 murders? What is P X 3 murders? What is P X 6 murders? Make sure to double-check your answers by the calculator functions: binompdf ( ) or binomcdf ( ). 3) What is P z 1.56? 4) What is the z-score that has an area of 0.65 to its left? R. Staple in order: TITLE PAGE, Session window, Histogram.