The national average for the math portion of the College Board's S A. T is 5 15 The College Board periodically re scales the test scores, such that the standard deviation is approximately 100. Answer the following questions using the a bell shaped distribution and the empirical rule for the verbal test scores. So we've got a a national average, so our average is shown with X, but the line over it and that's it. Five 15 with a standard deviation of 100. So if we use your typical bell curve here, where right here, this would be your average at 5 15 and then one standard deviation above the standard deviation is 100. So you just add the standard deviation of what you had their need out of six 15 another standard deviation 7 15 and then our final standard deviation. You usually do three standard deviations above and then three below 3 15 and then one more to 15. I'm still getting used to this program, so that's why the handwriting's not fantastic. So port A. That's an A not a nine. Ah, what percentage of students have an S a T math score Greater than 6 15 Well, first thing we want to understand is that this chunk right here represents 34% 0 hang on. Sorry. Let's just change that to smaller area. This is about 34%. This is also a 34% chunk making this entire section right here. 68% of you know of people. But what this represents is 68% of people that take the S A T usually score with within 415 as their score and 615 is their score 34% from here to here. On the other, 34% are from here to here. Um, over here, this little chunk right here is going to be at 13% as is, actually, let's use a different color for that in my classroom. I like to color code, so let's go ahead and color code. This is a 13%. This one is also 13%. So if you were to take all of this and you have 68 through this part plus 13 which is, um, 81 plus another 13 which is 94. So 94% of people well usually score between 3 15 and 7 15 on their exam and then to person. So sorry again. Another color. We want 2%. 2% here, 2% here. Meaning? I'm gonna go underneath for this just so that I have enough space. Meaning that so 94 plus 2 96 plus no. To 98% of people. 98% of people score between 215 and 2815. So that is all important to know, to be able to answer these four parts right here. So what percentage of students have an ace and s a C mask or greater than 6 15? So six fifteens right here. And we want everything greater than that. Right? So we've got the 68%. What? Well, here, let's go this way. We've got 100% of people fall under this curve, and then that means that 100% minus the 13 minus the two is some 100 miles. 15 is about 80% 35%. And then there's, like, 0.1% over here. So I'd say that's negligible. Your most people aren't going to be out here way up here or way down here. So we'll say approximately 85% are Ah. Okay, 85% score lower than that. So 15% approximately 15 percent. The students score 6 15 or greater on the S. A T. Part B is asking what percentage of students have an S A T math score greater than 7 15 So now we're looking here. That's about 2%. So about 2% a student score greater than 7 15 So you can see the questions they're going actually relatively quickly, because we were able to set this whole chart up, and that's pretty much where all our works gonna be. What percentage of students have an S A T mask or between 4 15 and 5 15 So I'm just going to race some of this. So if you needed to watch or see any of that, you can just go back in the video eso between 4 15 and 5 15 What percentage of students have an S a T mass score between here and here? Well, between 4 15 and 5 15 is 34%. So about 34% of students score between 4 15 and 5 15 on the math portion of the S a T. Then finally, part D Ah, What percentage of students have an S A T math score between 3 15 and 6 15 So again, let's just go ahead and get rid of this line here so that we don't have too much going on here. So between 3 15 and 6 15 So you take all those percentages in there. He got 13% up there. I'm sorry. That's gonna 13%. You got a 34% and another 34%. That 68% plus 13. That would be 81%. So about 81% of students score between 3 15 and 6 15 on the S A T math test.