Binompdf and binomcdf functions | Random variables | AP Statistics | Khan Academy

What we're going to do in this video is use a graphing calculator to answer some questions dealing with binomial random variables. This is useful because if you're taking the AP Stats, the Advanced Placement Statistics test, you are allowed to use a graphing calculator, and so this could actually save you significant time.

It says here I have a 0.35 probability of making a free throw. What is the probability of making 4 out of 7 free throws? Well, this is a classic binomial random variable question. If we said the binomial random variable X is equal to the number of made free throws from seven, I could say seven trials or seven shots. Seven trials with the probability of success is equal to 0.35 for each free throw.

So really, this question amounts to what is the probability that my binomial random variable X is equal to 4? Now, what we're going to see is we can use a function on our TI-84, not named binomial C, or binom PDF, I should say. Binom PDF, which is short for Binomial Probability Distribution Function. What you're going to want to do here is use three arguments.

The first one is the number of trials; so in this case, it is seven. If you're doing it on the free response section of the AP test, you should make it very clear that that right over there is your n. The graders will actually look for that to make sure that you're not just, you know, guessing what goes where. So you'd say that is my n, and then you would say your probability 0.35.

Once again, if you're taking the test, you should mark that that is your p. Lastly, but not least, what is the probability that a binomial variable, when you're taking seven trials with the probability of success of each of them being 0.35, that you have exactly four successes?

Now let's get our calculator out and actually do that. All right, so now we have our graphing calculator out. There are a couple of ways to input this. You could just type it in directly; that could take time. You could do second and this little blue distribution here. So there you have it. In order to get to the function, you could either scroll down or you could scroll up to get to the bottom of the list, and you see it right over here: binompdf.

You could do alpha A to go there really fast or you could just scroll up here, click enter, and then you have the number of trials that you want to deal with. Well, we're going to take seven trials, the probability of success in each trial is 0.35, and then my x value—well, I want to find the probability that my binomial random variable is equal to four, four successes out of the trials.

Now let me go to paste, and this is actually going to type in exactly what we had before. Notice this is the exact same thing. So I have seven trials, p is equal to 0.35, and I want to know the probability of having exactly four successes. Then I just click enter, and I get—there you go—0.14. So this is equal to approximately 0.14.

Now based on these—the same binomial random variable—if we're then asked what is the probability of making less than five free throws? So we could say this is the probability that X is less than five or we could say this is the probability that X is less than or equal to four.

The reason why I write it this way is because using it this way, you can now use the binomial cumulative distribution function on my calculator. If I just type in binom—and once again I'm going to take 7—or binom CDF, I should say, cumulative distribution function—and I'm going to take seven trials and the probability of success in each trial is 0.35.

Now when I type in 4 here, it doesn't mean what is the probability that I make exactly 4 free throws; it is the probability that I make 0, 1, 2, 3, or 4 free throws. So all of the possible outcomes of my binomial random variable up to and including this value right over here.

So let me get that. Let me get my calculator back. So once again, I can go to second distribution. I'll scroll up to go to the bottom of the list, and here you see it: binomial cumulative distribution function. So let me go there, click enter, and once again, 7 trials, my p is 0.35, and my x value is 4.

But now this is going to give me the probability that my binomial random variable equals 4. This is going to give me the probability that I get any value up to and including 4, so this should be a higher probability. And there you have it; it is zero, approximately 0.94.

So this is approximately 0.94. So hopefully you found that helpful. These calculators can be very useful, especially on something like an AP Stats exam.