### Binomial Distribution

Binomial Distribution

Project 2

Distributions

1. Peruse (check out) my example. I entered my data in sheet 1 on row 1 (52% is pitiful). Then, I compute the number of successes in 10 trials beginning from the first shot and entered that number (4 makes) in cell B2. I continued by computing the numberof successes from attempt 2 through attempt 11. Again this equals 4 and I entered that in B3. Continuing along, I have a row from B2 to CN2 with the numbers of makes in 10 trials. Next, I computed the frequency of each of these numbers and entered that where it is labeled “binomial distribution. Finally, I plotted the frequencies. It’s somewhat bell-shaped, but not exactly. The reason is, of course, that this is only a sample.

2. Binomial Distribution: number of successes in n trials. (If you are a “spreadsheet wizard,” you can have the spreadsheet make these calculations.) Here is the manual way to do it.

a. Count the number of successes in the first 10 attempts.

b. Count the number of successes from attempt 2 through attempt 11.

c. Count the number of successes from attempt 3 through attempt 12.

Etc.

d. Count the number of times (frequency) that you had 0 successes.

e. Count the number of times that your had 1 success.

Etc.

f. Plot the binomial distribution. (Successes along the horizontal – frequency along the vertical)

g. Compute the mean and standard deviation.

3. On sheet 2 is my geometric distribution. Here again, I entered the data on row 1. Then I compute the number of trials until success. You can see that my first make was on the second try; so the number of trials until success (starting from the first shot) is 2. I again calculated the frequencies and plotted the distribution. It looks fairly close to geometric.

4. Geometric Distribution: number of attempts until next success.

a. Count the number of attempts until your first success.

b. Starting from the second attempt, count the number of trails until your first success. (note: if you first success is on attempt 6, then the answer to part a. is 6, and the answer to part b. is 5.)

etc.

d. Count the frequency of “success on first attempt.”

e. Count the frequency of “success on second attempt.”

Etc.

f. Plot the geometric distribution (attempts on the horizontal – frequency along the vertical)

g. Compute the mean and standard deviation.

5. Turn your work into the dropbox. Specifically, you will turn in a spreadsheet file.

Project 1: Data

1. Shoot 100 free throws

a. You may choose another activity (e.g. six foot putts; archery target; goal kicks in soccer; hockey penalty shots, etc.)

b. The activity must have a dichotomous outcome: success or failure.

c. Choose an activity such that your success probability is somewhere between 0.3 and 0.8.

d. Do the 100 attempts in on session. (Rest is allowed.)

e. Try to be successful, but don’t worry. There is no reward for higher success percentages.

f. Don’t make up the numbers. There are statistical tests that identify made-up data.

2. Record the data (1 for a make; 0 for a miss) on the data sheet.

3. Enter the data on a spread sheet.

a. Put your name in A1

b. Enter the data as a series of 1’s and 0’s from B1 to CW1

4. Save. Do not turn anything in at this stage.

Data Sheet

1. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

2. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

3. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

4. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

5. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

6. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

7. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

8. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

9. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

10. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

Enter the data on the first row of a spread sheet. Your name in A1. Your data (1 for a make, 0 for a miss) in B1, C1, etc.