Okay for this problem, We're gonna compare some test scores. So we've been told that two different students equal not a points for their test force, but we're gonna try to use these scores. Our plan is to use, uh, Z scores to see who did better relative to the rest of the class and just did better overall. So test scores. We had some information that test one had a meaning of 65 standard deviation of 10. And for test two, that had a mean of Okay. Okay. 80 and a standard deviation of five. So we're gonna do is we're gonna look at each student's test scores and do this the Squire, both of those. So the students names are Derek and Julie. Get Dirks thescore here, and we'll get Julie easy score and see who the winner is. So because there's so many calculations and when he does my calculator over here. So, um, wait. Told Derek that eighties on both tests, So we're gonna take a score. It's backed away that mean for that first test and divided by the standard deviation of further first test. So that means he has of these squirt 1.5 on the first test. And for the second test, you got an 80 again, Mr Consistency. And the the extended deviation for that one. It's taking away 80 and actually zero since he got the meat zero. Well, before my calculation outside. Got a zero. These four on that for Julie. She, uh, did well in the first test, so she had 70 minus 65. First test, maybe a little bit harder. Um and so she had an overall there. A 0.5. The score for test one and four. Test to shed much better. She got a 90 but no test, too, with a little bit heart with a little bit easier. So she 10 points better than the mean in the variations Little assets to so putting all the pieces together, we can get that. Answer the question. So for Derek, he had a Z score of the first test of 1.5, and on the second test, he had a Z score of zero. He hit the mean Julie had a Z score of 0.5 in the second test. She had a Z score of two and we can actually add this together. It's their combines. The score. So overall is the scores 2.5, whereas his overall Z score was only 1.5 z for combined. So even though they have the same amount of points of the problems stated relative to the rest of the class and standardized, Julie actually did better. Eso Julie will answer the question. Julie had better test results. Overall, Ask the purpose of these Forced gives an idea relative to the rest of the class.