 Hi this is Dr. Don. I want to go over a problem about a probability distribution that you can solve very quickly using stat crunch. In this question we're told that students take a quiz with eight questions. The number of questions they answer correctly x can be approximated by the following probability distribution. And they give us a little table here of the values of x from 0 to 8 and the probability of getting each of those numbers of questions correct. You can do this very quickly using stat crunch. I'm just going to go open stat crunch. We have our data loaded into stat crunch. The first variable x are our values of the number of questions that could be answered correctly from 0 to 8. And the second p of x is the probability of each of those answers occurring. Again this is a discrete distribution. You should know that because these are integers 0, 1 through 8. But let's solve it and we're going to go to stat calculators down at the bottom custom. Our values are x values in that column are weights or our probabilities p of x. And we click compute and we get this nice little custom calculator that jumps up. And you notice down here that we're given the mean which is one of the answers that we had to find. And the standard deviation which is one of the answers we had to find. The other answer that we needed the variance is just be the square. So we just take 1.777 square it to get the variance. One of the things I'm going to show you though is once you get this custom calculator you can answer more questions about them probably. Which this particular problem that we have doesn't ask those questions. But for example what's the probability that student answers more than 3? Click compute and it's 90% probable that a student will answer 3 or more questions correct. And you can answer a lot of questions like that. So this little custom calculator is really a handy thing. It saves a ton of time. Hope you learn how to use it.