 Hi, this is Dr. Don. I have a problem out of Chapter 5, Section 3, about the normal distribution. In the problem, we're told that we have a sample of 100 obese young adults. We're told that the population of young obese adults has a mean of 322 and a standard deviation of 90. They give you a link to the table, but if you use stat crunch, you're going to save yourself a lot of heartache and mistakes. The first question is, describe the sampling distribution of X bar, which is just the mean of the samples. Remember that the mean of the sampling distribution of X bar is equal to the mean of the population, which is in this case mu of 322. The standard deviation, sigma sub X bar of the sampling distribution though, is not equal to the sigma 90 of the population. Remember the formula that you need to use is the sigma sub X bar is equal to sigma divided by the square root of the sample size. In this case, our sample size in is 100. Square root of that is 10. 10 divided in 90 gives us 9. With that, we can answer the next question, which is describe the shape of the sampling distribution of X bar. Remember, because of the central limit theorem, if we have a large enough sample size, a large enough n, and we generally say that's 30, then the distribution of the sampling distribution will always be approximately normal regardless of the distribution shape of the overall population. Okay, let's get in these last two questions. They want us to find the probability that the overall mean physical activity is between 300 and 310. And then the second part is the probability that the mean physical activity is greater than 366. You can really step on yourself trying to do that in the table. So let's bring up stat crunch. Remember, if you're in my stat lab on almost every problem we do, if you click on question help, there will be a link that will take you to stat crunch. But if you happen to run into one where it is not available that way, you can go to statcrunch.com and log in there using your my stat lab credentials, and you can access stat crunch that way. Once we get into stat crunch, on most of the problems we do in this course, we're going to start with this button right there, the stat button. And here we want to go to calculators and we're going to find the normal distribution calculator. And the great thing about stat crunch for these type of problems is it draws a sketch for you, which will help you make the dumb dumb errors that we're all likely to make. We need to put in the mean because we're not using the standard normal distribution, which has a mean of zero and a standard deviation of one. Our mean here is 322. Our standard deviation on the sampling distribution is nine. And the first thing we want is the probability that the mean physical activity is between 300 and 310. The calculator has a neat little between button. We click on that, the mean and standard deviation don't change. And we just enter our 300 and our 310, click compute, and we get a probability between those two values. You can see it right there, the red area of .084. The second part is the probability greater than 366. We go back to the standard, click on the standard button, and we want to select the greater than side. We want to be pointing to the right for greater than. And we put in 366, click compute, and we get a probability of .0005. You can't even see the red area. It's so small out there. So our answer to four decimal places would be .000. And one final comment. Remember probabilities always have to be between zero and one. They can never be greater than one. And I see that too often in students. They will report a value like this student did of greater than one or less than zero. So hope this helps.