Computing binomial probabilities with Minitab

Computing binomial probabilities with Minitab
You can compute binomial probabilities with Minitab in the following way.
Suppose you have a binomial distribution with 15 trials (n=15) and probability of
success p=0.7. In the following you will see how to compute probabilities of
exact events and cumulative probabilities with Minitab.
For example to compute the probability of exactly 5 successes you go to: CALCand
choose Probability Distributions – Binomial in the drop menu. Press
OK.
Choose “probability” in the window that opens, then type in the number of trials
(n, so 15 in this case) and the probability of success p (i.e. 0.7) in the “event
probability” box.
You may have the value for the number of successes inserted in a column in
which case you refer to it in the “input column” box, or you can type the value
in the “input constant” box. Press OK. (see screen shot on next page)
The result will appear in the session window in Minitab.
Here is the session output:
Probability Density Function
Binomial with n = 15 and p = 0.7
x P( X = x )
5 0.0029803

To compute cumulative probabilities, you check the “cumulative probability” box
in the binomial distribution window.
For example, the probability of at most 10 successes, is PX≤ ( 10) = 0.4845 .

You can also generate the entire table of probabilities with Minitab. Start by
typing the values of the number of successes in a column, say C1. If you work
with the same binomial model with 15 trials you will have to insert all values
from 0 to 15. You can do this more efficiently by using CALC- Make Patterned
Data – Simple Set of Numbers.
Fill in the boxes in the window as see in the next picture and press Ok.

So you are asking Minitab to enter all values from 0 to 15 in the column C1. You
will see the values appear in column C1. Next you use the probability
distributions command (as described above) to compute the probabilities
associated with the values in column C1, only that instead of using “input
constant” box you use “Input Column” and select C1. For storage specify a
different column, say C2. Press Ok. You will see the probabilities appear in
column C2 in your worksheet.
Unfortunately Minitab cannot draw the histogram of the data if it is given in two
columns out of which one contains the probabilities associated with the values in
the first column (or at least I haven’t found that out yet).
Surprisingly enough this can be done with TI83.
One way of getting the histogram of a binomial distribution is to generate
random data following the given model and construct a histogram of the data
generated.
Here are the steps to do just that. We will generate 1000 values from a Binomial
model with 15 trials and probability p=0.7 of success. That is, Minitab will
generate 100 rows of data that will represent the number of successes out of 15
trials.
Choose CALC- Random Data – Binomial. Enter the number of rows to
generate (1000 in our case), specify the number of trials and the probability of
success as well as the column where you want the data to be stored (C3 on our
screen). Press OK. See screen shots on next page.

Then, using STAT – Basic Statistics – Display Descriptive Statistics you
can perform the descriptive analysis of the data that was generated and you may
add to it a graph (histogram of the data for example).