MAT 223, Excel Lab Project #3, Fall 2015
Name __________________________________
General Directions: This lab uses Excel to create discrete (binomial) distributions, and to create graphs
of these distributions, as well as calculating statistics on these distributions, such as mean and variance.
The ideas we develop here will be important in later chapters when we require our binomial data to be
approximately normal.
Part 1. Creating Binomial Distributions in Excel.
1. Begin in cell A1 and type into the cell “Success”. In cell A2, type “0”. In cell A3 type “=A2+1”.
Copy cell A3. Highlight down the A column and paste the formula into the cells down to A22.
You should get a list of values from 0 to 20.
2. In cell B1 through D1 label these columns “Distribution 1” through “Distribution 3”.
3. In Column B we are going to create a distribution with 20 trials, and a probability of success 𝑝 =
0.1. In cell B2 type “=binom.dist(A2,20,0.1,FALSE)”. Note that the syntax here is different than
we have in our TI calculators. The number of successes is listed first, then the number of trials,
then the probability. The FALSE tells Excel that this is not a cumulative distribution. Copy and
paste this cell into cells B3 through B22.
4. In Column C, we are going to follow the same procedure, but we will let 𝑝 = 0.5. Finish by
copying and pasting the cells into C3 through C22.
5. Repeat the process again in Column D with 𝑝 = 0.85 and copy the formula into cells D3 through
D22.
6. Create a graph for each of the three distributions (a column or a line graph will do), and copy
and paste the graphs below. Use those graphs to answer the questions that follow. Be sure
that each graph is labeled with the distribution details, axis labels, and other features of a good
graph.
7. Calculate the expected value of the distribution: go to cell E2 and type “=A2*B2”. Copy this
formula into the cells E3 through E22. Repeat the formula in cell F2 as “=A2*C2”, and in cell G2
as “=A2*D2”. Copy these formulas down the column.
8. In cell E23, type “=SUM(E2:E22)”. Copy this cell into F23 and G23. These values are the
expected values of the distributions.
9. To calculate the variance, repeat the above steps in the next three columns. In cell H2 type
“=A2^2*B2”. Copy the formula into the cells in the column from H3 through H22. Make a
similar adjustment and repeat these steps in columns I and J for the remaining two distributions.
As in step #8, sum the entries in the columns.
10. To complete calculation of the variance, in cell H24, type “=H23-E23^2”. In cell I24, type “=I23F23^2”. In cell J24, type “=J23-G23^2”. These values are the variance.
Part 2: Questions
1. Record the values of the mean/expected value and the variance for distribution 1 here:
2. Record the values for the mean/expected value and the variance for distribution 2 here:
3. Record the values for the mean/expected value and the variance for distribution 3 here:
4. For each distribution, compare the calculation 𝑛𝑝 for each distribution to the expected value we
calculated in 1-3 above. [Recall that 𝑝 varied for the distributions, but 𝑛 = 20 for all of them.]
Do the values you find agree with the graphs? Why or why not?
5. For each distribution, compare the calculation 𝑛𝑝(1 − 𝑝) for each distribution to the variance
we calculated in 1-3 above.
6. For each distribution, determine whether the distribution shape is symmetric or skewed. If the
distribution is skewed, is it right-skewed or left-skewed.
7. Find the value 𝑛(1 − 𝑝) for each distribution and record those values here.
8. Using the information gathered above, which of the distributions have both 𝑛𝑝 ≥ 5 and
𝑛(1 − 𝑝) ≥ 5? What is true of this(these) distribution(s) that is(are) not true of the other(s)?
Part 3: Experiment
1. Using the model we created in parts 1 and 2, repeat the exercise by creating your own
distribution experiment. Start on a new sheet. Create a distribution with 50 trials or more.
Choose three different probabilities for success. For best results, choose one probability less
then 0.1, one probability greater than 0.9, and one between these values. Repeat the Part 1
steps to create the distributions, create graphs of the distributions, and calculate the expected
value/mean and the variance.
2. Paste the graphs you created below.
3. Record the values of the mean and variance for each distribution here.
4. Following the questions in Part 2, do these distributions follow the same pattern seen with the
original three distributions? Why or why not?
5. Go to the normal distribution grapher found at
https://www.statstodo.com/NormalPlot_Pgm.php
Choose one of the graphs that appeared the most normal (either my example with 20 trials, or
your own), and enter the mean/expected value and the standard deiation we calculated for the
distribution (take the square root of the variance). Copy and paste the graph obtained here
(you may need to do a screenshot). How does it compare to the binomial graph of the
distribution.
6. On the same site, do the same thing for one of the skewed graphs. Paste the normal graph you
obtain here. What do you notice about this graph compared to the binomial one? Is the normal
distribution a good model for what we obtained? Why or why not?