Math 227



Math 227 Minitab Lab

Mrs. Renee Butler Ch 4

#1. Consider the following data of computers in schools. Elementary and secondary schools were classified by the number of computers they had. Calculate Relative Frequency Probabilities and answer the following questions..

Number of computers (X) Frequency [pic] Relative Frequency Probabilities

1 to 10 3,170

11 to 20 4,590

21 to 50 16,741

51 to 100 23,753

100 plus 34,803

a) Copy the above chart with the relative frequency probabilities you obtained from the Minitab worksheet.

Choose one school at random. Find the probability that it has….

b) more than 100 computers.

c) 20 or fewer computers.

d) no more than 50 computers

e) Give the formula for Empirical Probability AND explain it in your own words.

#2. a) Simulate rolling a single die by generating 5 integers (5 trials) between 1 and 6. Count the number of 2s that occurred and divide that number by 5 to get the empirical probability. Based on 5 trials, what is the probability of getting 2s?

(note: your answer will be different from others because this is empirical probability.)

Copy your tally for the ‘counts’ and ‘percents’ and highlight your answer.

b) Repeat (a) for 25 trials. What is the probability of getting 2s?

c) Repeat (a) for 50 trials. What is the probability of getting 2s?

d) Repeat (a) for 100 trials. What is the probability of getting 2s?

e) Repeat (a) for 500 trials. What is the probability of getting 2s?

f) In your own words, generalize these results in a restatement of the Law of Large Numbers. (Look in your notes and your book at the definition of Law of Large numbers before you answer this question in your own words.)

#3. Simulate 50 births, where each birth results in a boy or girl.

a) Copy your tally for the ‘counts’ and ‘percents’.

b) Based on the result in (a), calculate the probability of getting a girl when a baby is born.

c) The probability obtained in (b) is likely to be different from 0.5. Does this suggest that the computer’s random number generator is defective? Why or why not? Answer in your own words. You may use your notes to help you.

#4 YOUR homework: Do these problems on Page 206 and include them in your minitab lab report on Chapter 4. (In the 4th edition book, it is on page 194.)

Page 206 # 37 & 38

#37 is like #1 above.

BEFORE you answer #38, FIRST, simulate flipping a coin 100 times using Minitab. This is like #3 above. How many heads did you get? What is the probability of getting heads from your simulation? Show the simulation and answer these two questions FIRST. THEN, do #38 in the book. Answer in your own words in a complete sentence.

How to Do it:

#1. Calculate Relative Frequency Probabilities from the table

1. In C1 enter the values of X and name the column X.

2. In C2 enter the frequencies and name the column [pic].

3. Select Calc>Calculator.

4. Type P(X) in the box for Store result in variable:.

5. Click in the Expression box, then double-click C2 f and click the division operator.

6. Find Sum in the function list and click on Select.

7. Double-click C2 f . (You should see ‘f’/Sum(‘f’) in the Expression box.)

8. Click OK.

#2 and #3

How to Simulate Random Data

1. Click on Calc>Random Data>Integer

2. You will generate_____ rows of data (enter the amount of rows you want)

For #2a, put in 5, for #2b put in 25, …… for #3, put in 50.

3. Store in a column (C1) or any column (C1) to (C10).

4. Minimum Value: enter minimum. For #2, the minimum number of a die is 1.

For #3, enter 1 for the minimum.

5. Maximum Value: enter maximum. For #2 the maximum number of a die is 6.

For #3, enter 2 for the maximum. (Let 1=boy, and 2=girl, or vice versa)

6. Click ‘OK’.

Now that you have the simulated random data on the worksheet, follow the next set of steps.

To Calculate Relative Frequency Probabilities from the original data in a worksheet.

1. Click Stat>Tables>Tally Individual Variables

2. Select the column needed (i.e. C1) in the Variables:

3. For Display click Counts and Percents. This will give you the information to answer the questions.

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