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(15 points) Of first-time college students who matriculate to a certain university; the odds in favor of having graduated in the top 25 percent of their high school...

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(15 points) Of first-time college students who matriculate to a certain university; the odds in favor of having graduated in the top 25 percent of their high school class are 2.9 to 1. Of transfer students who matriculate to the same university; 0.5 proportion graduated in the top 25 percent of their high school class_(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class is (rounded to three decimal places)(b) For transfer students, th

(15 points) Of first-time college students who matriculate to a certain university; the odds in favor of having graduated in the top 25 percent of their high school class are 2.9 to 1. Of transfer students who matriculate to the same university; 0.5 proportion graduated in the top 25 percent of their high school class_ (a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class is (rounded to three decimal places) (b) For transfer students, the odds in favor of having graduated in the top 25 percent of their high school class are to 1_



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The College Board reports that 2$\%$ of the two million high school students who take the SAT each year receive special accommodations because of documented disabilities Angeles . Times, July $16,2002 ) .$ Consider a random sample of 25 students who have recently taken the test.
(a) What is the probability that exactly 1 received a special accommodation?
(b) What is the probability that at least 1 received a special accommodation?
(c) What is the probability that at least 2 received a special accommodation?
(d) What is the probability that the number among the 25 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated?
(e) Suppose that a student who does not receive a special accommodation is allowed 3 hours for the exam, whereas an accommodated student is allowed 4.5 hours. What would you expect the average time allowed the 25 selected students to be?

Already. So this question asks us about a pool of 10 schools, seven of which have an average G p a greater than 3.5 and for all questions will be considering a sample oh, size two from this pool. So part ay asks in this sample. What is the probability of getting exactly one school with a G p a higher than 3.5? So this is a hyper geometric problem. So our probability ISS They're seven schools with high GPS. We want one of them and then there are three schools without the high G p A. We want one of those over. There are 10 possible schools to pick from, and we want two of them for the sample and that is 0.4667 Part B asks for the probability that both schools in the sample have the high G p a. So that ISS, they're seven schools with high GPS. We want two of them. Then there are three schools with low GPS and we want none of them anger. They're 10 total schools and we want two of them for the sample, and that turns out to also be 0.46667 in part C. S. What is the probability that neither of the schools in the sample have the high G p A. And that is seven schools with high G p A. We want times three schools without the high G p A. And we want two of those all over the 10 total schools, and we picked two of them for the sample and that is 0.6 67

This exercise is once again looking at S 80 schools. But this time looking at how we can use an S A T to predict a GPS and a late gentile people could perform a college level. So part a asked us to write the equation of the regression light. Now, everything we need for this is given in the question. So we are predicting our g p a. They want g p A. Remember the hot to say it's a prediction predicted g p A is now are a value is given by the intercept Kerr fish and the question so minus 1.26 to remember the minus side and then our s a T coefficient is again given to us for the positive. No point no to no, not 21 for that city. Uh, that is old neat moving on pop be asked us to explain what the Y intercept of this Russian line indicates. Now Warren stepped is given to us hit now Usually in this imminent in any context, the won't set would represent predicted G p a. When s a T equals zero. Um, but it's hard for that toe kind of make any sense in this context because we've got a negative number as the intercept. But it does indicate a predicted debate when a city is zero and then looking at C l sister interpret this slope, which is this done? So what this is saying is for inch one point set in groups, we would predict E g p a. Increase off that value of the slopes off. No point, no, no to want full quints. That's what that means. So we will probably miss asking us to predict the GPS. A freshman who scored a combined 21 hundreds on This is just substituting into the equation we worked out in part A. So I predicted GDP is one point minus 1.262 plus no point, no North 214 as a very substrate in that 2100 these two moles plan together, come to four point for no for So if we have negative one point 262 that's 4.494 that is gonna come to three point to three to So the answer point for Part D and finally looking at Part E on it not finally looking at high, it says, Based on the statistics, How effective do we think SAT schools would be in predicting academic except success during the first most of the freshman year up to college? So the best indicator of this a one of the best and kids to this is our r squared value, which we given as 22.1%. Now it's showing that 22.1% of the variability in GP A schools in the first Master can be explained with this model so it could be explained with the S A T schools. Why was no high? It says it can give some indication. So I'd say Molterer indication. So while it shouldn't be used to fully gauge what people are gonna get, it can give you some kind of idea. But yeah, 80 well, 78.9% of very billeting do free schools could be explained with other things, so it definitely shouldn't be taken as everything that goes towards GP a school now in the last five, it says. As a student, if one it says as a student, would you rather have a positive or negative residual in this context. So? So that s manager about the or residual is Ah, actual or observe school minus are predicted school. Now, I did a We'd want the actual school three o'clock as possible. So for if our actual scores higher than I predicted, in other words, we did better than they thought. That would be groups and indigent that Gregson zero. So we'll be looking a positive residual. And I was a student. You definitely will, Max, if you get a negative residual.

Okay, so we're supposed to calculate a grade point average here and this student a 4.0, which is the AI has nine credit hours. Is it four point now? 1500 hours and B, which is a 3.0, 33 hours a majority of that time or the majority of the classes, I should say, at a C in three hours of the D. And so basically, these numbers are not the weights these air. Actually, what's going to be average? The 4321 in the four has the weight of a nine because that's how much of the time or the classes have received that four. Or that a. And so that's how I had placed this in this right here is the weight, and these are the actual numbers that go into computing the great point average. So once I did that, I cooked equal average. Of course, in Google Sheets, Microsoft Excel works as well. And then I had added the first column comma Highlight the Second Column, and this year has Theo exact minimum grade point average of 2.5 needed to stay at that school. So, yes, that student is okay to say that school, but barely has a minimum G p a

Nortel students in 2013. Ah, but 206.9 million now consider number of elements in sample space that is an SP 202 106 million 900,000. Now in part A. We need to find the number off people having advanced degree. So 11.6% off tortas total people north over 206 million 9000 900,000. So we need to find the number of people that had and that are having advanced degree. So 11.6% off 206,900,000. After calculation, we get 24 million and 400 so that there were total 24,000,400 people having advanced degree nine Part B Let us consider that even e be the person selector has on ah, bachelor or higher degree. So as we can see that among Tortola off 100 students there were 20.1% having best no degree and 11.6% having higher degree. So storper 31.7% off Corpus Children's would and this so we can see that there are a total 31.7% off 206 million people having bachelor or a higher degree now to find the probability off, even e probability off even ease talk. Be one among 100. So 0.317 since they ever toward shelter even 0.7 persons off even E among total of 100 persons since starting 1.7% off, 206.9 millions are given. So this is the probability that even ease opening. Nine Bart See conceded FB number off People having high school diploma on g B die Even that number off people I I doing post secondary education. What haven't in post secondary education? No, we know that number off people or number of elements in fr 29.8% off Tortola total are 209 to 6.9 million and number off people in the venti, or number of elements in even G R. Since the number off people um, having postsecondary education are 16.8% plus 9.8% plus 201 20.1% plus 11.6% so adding all these we get number off people completed post secondary education or we're doing post secondary education were 16.8 percent plus 9.8 person bless 20.1% plus 11.6% off portal and portal over 206.9 million. No to find the probability that even F r D is occurring so we can find probability off after you and Angie, since these two events are mutually exclusive. Therefore, we can write probability off F plus probability off G. Therefore, our ability off efforts 29.8 over 100 plus reliability of G is adding all these times we get 58.3% off 206.9 million, therefore probability of jeans 58 points, three over 100. So the total probability will be you did 0.1 over 100 which is 0.881 nine party Consider the even at their upper son has aren't our degree so number of elements in even you are. We can say the number of persons aren't our degree are number of persons are associate degree, last number of persons aren't bachelor's degree and the number of persons are at one's degree, adding all these bigot 9.8 person blessed 20.1 person plus 11.6 person off Tortola. That is 206.9 million now, adding all these big 41.5 person. So a probability off, even at brokering is 41.5 over 100 that is 0.415 This is a probability that a person selected at random are their degree.


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