We'll begin by interacting with the applet below to get a feel for how different values of and affect the distribution of our probabilities for a Binomial distribution.
is the number of trials of a Bernoulli experiment (an experiment with only two outcomes, a success or a failure)
is the probability of success of each trial and each trial is independent.
Begin by setting the applet to and .
How would you describe the distribution of the graph you see?
Remember when describing the shape of a histogram we use the phrases positively skewed, symmetrical and negatively skewed.
Keeping , change the value of . Does your description of the distribution stay the same?
In both cases, with , you should see that the graphs are symmetrical.
This makes a lot of sense! A value of indicates an equal probability of success and failure, so you'd expect symmetry.
Now set the applet to and and slide the value to the left and to the right.
Now slide the and values around and confirm that those findings about the shape of the distribution hold for all scenarios.
Let's look through a series of screenshots to do these problems using the TI-Nspire.
Firstly through the menu we select Statistics and Distribution and select BinomialPdf to calculate when and
To calculate the cumulative probability of we select BinomialCdf instead.