 Hi, this is Dr. Don. I have a problem out of chapter four, probability distributions. And this one we're told that 23% of students say they use credit cards because of a rewards program. You randomly select 10 students and ask them the name of the reason they use credit cards and then find the probability that the number of students who say they use credit cards because of their rewards program is exactly two, more than two, between two and five. Well, this is a binomial because we're given a proportion, 23%. And when we ask students and if we're interested in only if they use because of their rewards program then it's either, it's a yes or no, success or failure, so it's a binomial. So the easiest way to do this is to use stat crunch. I've got stat crunch open over here. We click on stat, calculators, binomial, bring up the binomial calculator. We need to enter our n, which is 10, we're okay there. Our p this time is 0.23, 23%. First question is a probability of two, so I'm going to enter two there and we want exactly two, so I look for the equal sign and I get 0.294 rounding to three decimals, which is the answer that went over here. The next problem is probability of greater than two. I've got two in there already so I'm just going to click on the drop down, find my greater than symbol and see that's 0.414 rounding to three decimal places, which is the answer there. Finally, it's between two and five and clues, which means we include two and we include five. So I go to my between calculator and I enter two and five and hit compute and I get a probability of 0.695, which is the answer they want here and you can see that this is the discrete two, three, four, five bars are read. So I hope this helps and if it does help, please consider subscribing to my YouTube channel, the stats files. Just click on the big red button.