Tutorial

Binomial Distribution

 

In this technology exercise you will learn how to use the TI-83+ to calculate binomial probabilities.

 

Part 1: The Tutorial.

 

Suppose we are interested in finding the probability of 0 through 5 successes from a binomial distribution where the probability of success on each independent trial is 0.90 and there are n=5 trials.

 

On the calculator press [2nd] and [DISTR].  Cursor down and select 0:binompdf(

 

 

The command binompdf(n,p,x) allows you to enter a specific value for n = the number of trial, p = the success probability, and x = the total number of successes for this experiment.  If we want the probability that there will be exactly two successes in this experiment with five trials, we type in:

 

 

And the probability is P(x = 2) = 0.0081.

 

You can also get a list of all the possible outcomes for a specified number of trial and success probability by using the command: binompdf(n,p), where n = number of trials and p = success probability for each independent trial in the experiment.

 

 

 

Store this list list in [L2] by pressing [STO] -> [L2].  The [STO] key is directly to the left of [1].

 

Next go into [STATS],  (clear [L1] if necessary first) select  1:Edit, and type in the number of successes 0 through 5 in [L1].

 

 

Looking at [L1] you can read down and see our list agrees with our previous calculation: P(x = 2) = 0.0081.

 

Suppose we are interested in determining the probability of at most 3 successes. Then, we want to find the probability of 0,1,2, or 3 successes. We could simply add the probabilities we find from our list, or we could find them all at once by using a different command.  We want to add 1E-5 + 4.5E-4 +.0081+.0729 = .08146.  If instead we use the command:

 

You can get the answer straight away! This command sums up the probabilities for you. Suppose you were interested in at least 4 successes. Then we want to find 4 or more, so we would add the probabilities for 4 successes and 5 successes. We can use the fact that the probabilities must add to one and the previous command.

 

 

This is a great help when the number of trials is large.