 Hi, this is Dr. Don. I have another discrete probability distribution problem that we can solve very quickly using stat crunch. And in this case, the problem is that we're told about the distribution of dogs per household in a small town. There's zero to five dogs. And we've got the probabilities listed below for each of those occurrences. They want us to find the probability of randomly selecting a household that has fewer than two dogs, a household that has at least one dog, and the probability of selecting a household that has between one and three dogs inclusive. So let's do it using stat crunch. We have the data now in stat crunch. And remember, we need to use the stat calculators custom to build a custom calculator. Our values of x are in the dogs column. Our probabilities are in the households column. And then I just click Compute, and it creates the custom calculator that shows us the probability of currents of each of those discrete values. Remember, it gives us the mean and the standard deviation of that distribution. And you can get the variance by just squaring the standard deviation. And it comes up and it shows the probability of getting less than or equal to zero is 69% roughly. Our first question, though, is find the probability of randomly selecting a household that has fewer than two dogs. So we click on the dropdown error. We want fewer than two dogs. I'm going to put two in there and click Compute. And the probability of getting fewer than two is 0.885. Note, you need to be careful of the wording of the question. The question said fewer than two. That means you use a less than operator. If it had said two or less, you would have used that operator and gotten 96% probability. The next question is the probability randomly selecting a household that has at least one dog. So at least means greater than. And since it says at least one dog, we want one in there greater than or equal to one is 0.311. And that is the answer they asked for there. Final question is find the probability of randomly selecting a household that has between one and three dogs. So we can use the Between tab here. And we want between one and between three, click Compute. And it's 0.288. That's their probability. So these custom calculators are really neat. Learn how to use them.