a. Use a computer (or random-number table) to generate a random sample of 56 M&M’s, using the corresponding theoretical probabilities for each color.

b. Form a frequency distribution of the random data.

c. Construct a bar graph showing the relative frequencies for each color. Use the same color order as in part a of Exercise 4.170.

d. Compare your experimental findings with the theoretical expectations.

e. Repeat parts a–d three more times.

f. Describe the variability you observe between the samples.

g. Consolidate your four frequency distributions into one frequency distribution having a frequency total of 224 M&M’s.

h. Construct a bar graph of the consolidation showing relative frequencies for each color. Use the same color order as in part a of Exercise 4.170.

i. Compare these experimental findings with the theoretical expectations.

j. Compare the consolidated findings with the four previous individual findings.

k. How does the law of large numbers impact this mini study?

MINITAB and Excel can only generate random numbers. Therefore, it is common practice to use numbers in place of the colors (words). Use the numbers 1, 2, 3, 4, 5, 6 to correspond to brown, red, . . . , blue, respectively.

MINITAB Release 14

a. Input the numbers 1-6 into C1 and their corresponding probabilities in C2; then continue with:

Choose: Calc  Random Data  Discrete Enter: Generate: 56 (# of M&M’s® in a pack)

Store in column(s): C3 Values in: C1 (color numbers)

Probabilities in: C2  OK

b. To obtain the frequency distribution, continue with:

Choose: Stat  Tables  Cross Tabulation & Chi Square Enter: Categorical variables: For rows: C3 Select: Display: Counts and Column percents  OK

c. To construct a bar graph enter the actual colors in C4 and the corresponding probabilities (%)

found in step b in C5:

Choose: Graph  Bar Chart  Bar represent: Values from a table  One Column of values: Simple  OK Enter: Graph variables: C5 Categorical variables: C4 Select: Labels  Data Labels  Label Type: Use y-value labels  OK Select: Data View  Data Display: Bars  OK  OK Excel

a. Input the numbers 1-6 in column A and their corresponding probabilities in column B; then continue with:

Choose: Tools  Data Analysis  Random Number Generation

 OK Enter: Number of Variables: 1 Number of Random Numbers: 56 (# of M&M’s® in a pack)

Distribution: Discrete Value & Prob. Input Range: (A1:B7 select data cells)

Select: Output range Enter: (C1 or select cell)  OK

b. The frequency distribution is given with the histogram of the generated data. Use the histogram Excel commands on page 61 using the data in column C and the bin range in column A.

c. Divide the frequencies by 56 to obtain the corresponding probabilities. Enter the actual colors in column D (ex. D13:D18) and the corresponding probabilities in column E (ex. E13:E18). To construct a bar graph, continue with:

Choose: Chart Wizard  Column  1st picture(usually)

 Next Enter: Data range: (D13:E18 or select cells)  Next Enter: Chart and axes titles  Finish (Edit as needed)