So we have information about the 2005 math s A. T. So it is called Meth S a T. And then I'll subscript at math and we're told that it has a mean of 520 a standard deviation of 115 and that it is basically a normal distribution. It's not exactly normal, but it's very close to one. And in part, A. We want to know what is the Z score. If somebody scores a 7 20 what is their Z score? Well, there is these scores what they got, minus the mean divided by 1 15. And so we see that that difference is 200. So let's take 200 divided by 115. And we find out that that is 1.7 roughly four. And that means that the person scored 1.74 standard deviations above the mean mhm. On the other hand, let's go the other way that we know that someone has a A Z score of 1.5 or the person scored 1.5 standard deviations above the mean and with them we want to know what was the person score. So remember the Z score is how many standard deviations above or below the mean So we don't know this score. But we know that this is true. And so with this will be multiplying 1.5 this value times 115 and then adding to that by 220 and we find out that the score would be 692.5. Now you can't get a 0.5 on the test, so it's either going to be a 6 92 or a 6 93. And Park Si is doing a comparison and they're dealing with the 2012 exam. And we know that the, uh, the S A T, assuming that it was math again, had a mean for that year of 514 and the standard deviation of 117 very similar to the previous when we looked at and the A C t, on the other hand, as a much lower point total. But the mean that year was 21 with a standard deviation of 5.3, and we have one person who scored on the S a t so we'll do that in blue on the S A T scored a score of 700 and on the other hand, the person on the scored a score of 30 and we want to know, relatively speaking, did which one did better? So let's find out. So let's go through and figure out what this s a T Z value is how many standard deviations above the mean so 700 minus 5 14. Divided by 117. And let me get that left front to see 700 minus 5 14. Divided by 1 17, the C score is 1.59 So this person scored 1.59 Standard deviations above the me. Now let's look at what happens here. What's the Z score here? And we have 30 minus 21 divided by 5.3. And once again, I'll go left front to see 21 books. I'm sorry. 30 right. Minus 21 which I already knew it was nine. I don't know why I don't just put nine divided by 5.3 and I can't do that. 5.3 division in my head and I get this. See, value is 1.698 So this is approximately 1.70 Standard deviations higher. So this person, relatively speaking, did a better job compared to others. Because this person has a score that is 1.7 standard deviations higher than me. And this one is only about 1.6 higher than the main. So this one is the winner.