 Hi, this is Dr. Don. I have a question out of Chapter 5 on the normal distribution and in this question we're asked to find the probability using the standard normal distribution, which is what we get out of the tables. And we want the probability of Z, and notice that the math operator is pointing to the left. So we want Z to the left of minus 2.74, or Z pointing to the right of positive 2.74. Now this student got the answer wrong. And if I click on that, you can see that the student answered 0.9939, which is the compliment roughly of 0.0062. So as usual, you should always draw the sketch. And here is my very rough sketch, but it will suffice. And you can see that I've got the standard normal curve with the mean of zero, and I put in minus 2.74 Z and highlighted everything under the tail to the left, out to infinity. And over here I've got plus 2.74 Z with everything under the tail and yell out to plus infinity. And that's the mistake that our student made. The student used this area here in between, because that's what is, you can easily get by mistake when you use the tables. So I'm going to show you how to do it using stat crunch. Okay, I've opened up stat crunch, and like with most of the problems we do, we start with stat button. This time we want calculators, and we're going to go down and get the normal distribution calculator. And it comes up, as I've said before, on the standard side, which means we're just going to find the areas on one side of the distribution curve here. It comes up with the standard normal mean of zero and standard deviation of one, and we're just going to leave that alone, because that's what we want to get the areas in the standard normal. I'm going to first put in minus 2.74, make sure that my math operator there is pointing to the left tail, which is what we want. Remember, we can change it to the left to right tail, click compute, and that gives me an area of .003 and a little bit more, and that's the area under the tail and red, which is matches what I showed you. Okay, now we need to get the area in the right tail. I'm going to change my operator to that side, and I need to change the minus to make it a plus, and we get the area in the tail over there is .003 again. So the total area is the .006. I'm going to show you very quickly another way that you can do it. There's a between, and this is a very useful calculator when you're given a problem with uneven Z values, and you want to get the area between them, which is what comes up in red, or because we're dealing with compliments, you can subtract that from one to get the area in the tails. I'm going to put in the minus 2.74 and plus 7.4, and that gives us the .9938, and you subtract that from one to get the .006, and of course these can be any values of Z to get the area between, and you can even have two negatives to get the area between. So be aware of that, it's a very useful calculator. I hope this helps.