Let's take a more visual look at the distribution and making the most of using it on our graphics calculators.
We'll begin by interacting with the applet below to get a feel for how different values of n and p affect the distribution of our probabilities for a binomial distribution.
n is the number of trials of a binomial experiment (an experiment with only two outcomes, a success or a failure)
p is the probability of success of each trial and each trial is independent.
Begin by setting the applet to n=10 and p=0.5.
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 p=0.5, change the value of n. Does your description of the distribution stay the same?
In both cases, with p=0.5, you should see that the graphs are symmetrical.
This makes a lot of sense! A value of p=0.5 indicates an equal probability of success and failure, so you'd expect symmetry.
Now set the applet to n=10 and and slide the p value to the left and to the right.
Now slide the n and p 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 P(X=5) when n=8 and p=0.3
To calculate the cumulative probability of P(1<=X<=3) we select BinomialCdf instead.