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Score: of 131 comdieiGi Hw Score: 7.6996 , 0f 13 pts 6.1.19-T Question Help Acompuny minulaciures wash-oiin motor Iha: of chargjo inthe food processng ndictn A tail: wahin thc lrat Tto mcto' i5 mareotod wth_ hcum operalon WafTn Enal glaran ee: mell Dulare aereet the Wash-dcin molors operate [Ciaced Ailio Tha nithor ppanamng Lht bolcro 'Jaire 140oo noura mitt Jppror Maley nCmeth miswbitad sandIrd devintiJn c( 3 Js0hdurs Whal tho prcoabilizy that = Wush-dotlinCo nenddn Wne: purcen1a3o of uash-down (rcy ol chalne MoorxCan neceu Ocakd for Inono Inan coneaanywank 7o0 houra? Cesn Wash-down mator - mor Fhan (Lplazedrea ofchatyja Eialard dezinbon Fazm'Mrta anal #Julz 47,350 hor? Aroroca Ialtt 0'0piztn ' belor Ialure Tnu probablilte ustc] mola RemEn charge IRounato 'our docimil Hcoe Mantad



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Find the percentile rank for each test score in the data set. 5, 12, 15, 16, 20, 21 What test score corresponds to the 33rd percentile?

So the first time he played, he scored X, and he has improved by 9485 points. Now he's scoring 11,000 and 53 points. So listen fact 9485 off both sides. Yes, but I think 11,053 subtract 9485. I get 1000. 1568 is what he scored his first try.

In this question, we're gonna be taking a look at the distribution of scores on achievement test using a relative frequency table and a percentile graph or a relative frequency graph. So we're going to start with our data and we're going to construct our team a lot of frequencies and then calculate a relative frequencies to make our graph. So relative frequency is just a fancy way of talking about percents. Cumulative frequency means you're just gonna add these numbers up. So we're going to bring the five over, and then we're going to keep adding them as we got so five plus 17 it's 20 to 22 plus 22 is 44 out on another 48 we get 92 add on another 22 or upto 1 14 and at on six, and that gives us a grand total of 20. So that means we are represented representing 120 pieces of data. So that is our end in this case, to find a relative frequency, we're gonna take each one of these cumulative frequencies and divide by 1 20 So, for our first interval five divided by 1 20 is approximately 200.4 So just to show you where that's coming from, I'm rounding these because we're going to be graphing on this graph where everything is estimated, so we don't have to be that precise. Eso 22 divided by 1 20 is 18% or 180.18 44 divided by 20th. About 440.37 or 37% 92 divided by 1 20 is about 77%. 1 14 divided by 20 is 95% and 1 20 divided by 1 20 is one. Now we're gonna graph this over here and we're starting with 1 96 But there are no achievement test scores below 1 96.5 So that's gonna get a zero. There's nothing before. And then as we go to the end of each interval, we're going to continue to build up our graphics. We move forward. So at the end of the next interval work, four percents about here at the end of the next interval were at 18% so just below 20% about here at the end of the next interval were at 37%. So about here, the end of the next interval were at 77%. So about here, the end of the next interval were 95% almost to the tall. And at the end of the last interval, we are at 100% now. One of the things that's important to know is that each of these intervals represents even other kind of knot standard ways with numb label, a scale they do represent consistently spaced out intervals. So I want to try to connect these with a straight line as much as I possibly can free so and this is what we make our cumulative frequency graph. Now, the reason we connect these with a straight line is because we are assuming that all of the achievement tests in the interval in between are evenly distributed. That's our best way of making a guess here. That may not be actually the case, but that's what we're going to use to make our estimation. Okay, so now we have our frequency graph curved, and we can use our frequency curve draft on. We can use that to make our estimates. So first thing that we want to estimate is what is the approximate percentile for somebody who scored 2 20 So to 17 to 2 38 to 59. What? Um, what we need to kind of know is how big that interval is. So we did say that they were evenly spaced on. That means that in between each of those intervals, we're looking at about 21 points. So each one of those lines is representing seven. So to 20 plus seven is to 24. So when I'm looking for to 20 I'm gonna be looking at the score of 2 20 It's gonna be about here, so I'm gonna follow to 20 up to the curve, and then I'm gonna follow that line over 2% all trying to draw this line a straight is that possibly can, and it looks like it's between 5% and 10% a little bit closer to 5%. So let's estimate that at about the sixth percentile, question B is asking for the percentile associated with a score of 2 45 So to 45 is going to be about here, Right? So about 7 to 38.7 about 2 45 about there. So again, we're gonna follow from a test score up to the graph and then follow from the curve over to the percent axis. So that looks to be at approximately 25. So about the 25th percentile. Her question. See, we're looking for the percentile associated with score of 2 76 So to 76 is going to be somewhere over here. So a little bit below to 80. I'm so I'm gonna estimate about here. You should not quite so straight there. Tried to even it out some of the end on. Then we'll move that over a little bit below 70%. So I'm gonna estimate that to be about the 68th percentile. These are just estimates. So if you're not exactly spot on, um, that's okay, that's that's a reasonable, uh, thing to happen with this kind of graph. So now what is the percentile associated with to 80? So, I mean, that's just like here, right? So we can kind of see that there's kind of a big gap that's happening there. So we're all the way up here now. All right, so we should really be drawing this line all the way down. This isn't much better done with a ruler on paper, then digitally, unless you were doing something like on Power Point or something. But we're above 75%. So maybe, like the 76 there, 77th percentile, and then the final score we're going to try to estimate the percentile for is 300. So three hundreds gonna be a little bit below here, and we're gonna follow that up a bit wonky. But it's a little bit before this line hears about their and then we're gonna follow that over, and we know that we're below 95% but not a lot below 95%. So maybe 94 93%. Ah, percent. All right, now we've got all those lines on there that we're gonna have to try to ignore a little bit, but we're gonna work the other direction, and we're going to try to, um, estimate the test score now given a percent. So if we have the 15th percentile, what is the approximate test for that goes with that? So we're gonna work in the opposite direction. 15th percentile. Follow that line over to the graph, and then we're gonna come down here and estimate. So we remember we said that each one of these lines is about seven. So this would be like to 24. This would be like to 31 2 38 So somewhere between 2 31 2 38 little closer, 2 to 31. So maybe, like 232 G. Um, we're gonna estimate that 29th percent up, so you can see, like, all this estimation, all we're going to be able to do is kind of guess right, the 29th percentile. Follow that line right below the 30th percentile over Teoh about here, maybe, and I will follow that down. And so this is to 38 to 45. The next one would be, what to 52. So we're a little bit before 2 50 like maybe 2 49 The important thing to kind of remember is that when you have the percentile, you work. You started to have relative frequency and work to the data. When you have the data, you started the data and you work to the relative frequency. Okay, so, H, we are looking at the 43rd percentile so the 43rd percent tells somewhere between 40 and 45 and we're going to come over to the graph over here and then follow that line down. And if this is to 59 this would be to 66. And so we're a little bit I don't know in the low in the low to sixties. So let's say like to 64 I were looking for the 65th percentile. So 65th percentile is here. Follow that over to the curve and then from the curve down. So it's gonna be a little bit above this line right here. So that was 2 59 to 66 to 70 three. So a little bit above to 73 I don't know. Let's say to 74 and then finally, the last one the 80th percentile. So we'll follow from the 80th percentile to the curve, but here, then we'll follow that down and like to 87 a little bit below 2 87 So let's say to 85. So, as you can see is the percentile was increasing. So where the test scores and that makes sense because we're accumulating more and more test scores as we go. Um, and the same was true here. The lower the test score, the lower the percentile that it was associated with.

Hi in this problem, a person takes an examination where there are about 100 questions and we have been given to situations how the person's goes based on the marks which are being awarded In case one for each correct answer, the person will get two marks and for each longer and sell one mark will be detected. And for each question that is left unattended, the person will be directed half market. So if the person takes an examination in this scenario, The person is getting a school of 135 And similarly we have another case wherein the person will be awarded to mark. Each poor character dances, half mark will be reduced to four wrong dances and one mark will be reduced to four questions which are left and attempted. So if this is too scenario, the person Is getting a score of about 233 and we have to find out how many questions has been left attempted. So let's form equations. Isn't this given information and try to solve for the number of questions that is left unattended, considering that there are about 100 questions let's suppose that we say X is the number of questions which which are correct, correctly answered and why is the number of questions which are wrongly answered And is there is the number of questions which are ah left un attempted? So if there is a case since we have about 100 questions, we can form an equation X plus Y plus, Is that equal 200. So this is the first equation. Now let's look at the case one in this case one we have, we know that there are two marks will be awarded for each correct answer, which means the total marks which are obtained by the person when when we're when a person uh answers X correct answers, It will be two works and one mark is reduced so therefore it will be minus white and half mark will be reduced for each question that are left and attempted. So therefore this will become -1, is that? And when you add all these things, he's getting a scorer 135. So we can read it this without the fractions by multiplying by two and when we do that we'll get four x minus two way minus is that this is equal to to 70 That this bigger equation # two. And now let's look at the case too and we formed the equation for case two as we know that for each correct answer is two months will be awarded. So therefore we ride on this as two weeks and half markets director for each wrong answer, that is minus halfway and one mark is reduced for questions left an attempted So therefore this is minus is it. And in this scenario the person is getting has scored 133. Let's relate without the fractions. So we and second multiplied by two, which means it will be four x minus boy -2, is that this is equal to 266. So let this be the equation number three. So now we have the three equations which is basically a system of equations in three variables. If we have this equation number one two and three We have three variables and we have to solve for. Is that because is there to present the number of questions which are left unattended? So our first task is to reduce the system of equations in three variables, stood two variables. How do you do that? What we can do is we can do it by elimination method. We choose one of the variable and eliminated from two equations twice. All right, so let's do that first so far that I'm going to take the first equation. Ah And I'm going to multiply before. You'll see why we have to multiply before. So let me multiply the first equation before when I do that, I'll be getting four x plus four way Plus four. Is it equals 200? Yeah. And I take the second equation as it is, I don't hear forex minus two Y minus. Is it equal to too salty. Now as we can see this we can if we do this attraction we can eliminate the X over here so far that we need to change the sign like this. This will be negative. So these four x and -4 x will get cancelled. So this gets simplified to six, Y Plus five. Is that equal to minus 1 70? Oh I'm sorry. So this has to be 400. This uh multiplied by four. This will be 400 and once again this will be minus And so 400 -2 70. So this will give us 130. And let's call this equation as equation number four. Now, in the same way we are going to eliminate X from the 2nd and 3rd equation as we can see that both equation has the coefficient of 44 X. So we can simply do the subtraction. So let's write the second equation here. Four X minus two minus. Is that He called 2- 17? And this one is for ex -Y -2, is it Equals to 66. So let's a practice, you can change the sign of this equation, this will become place, this will become plus and this will become negative. So now you can see that four x minus products will become zero and this is minus two, Y plus y is minus way and this is minus y minus. Is it plus two? Is there? Is plus is it? And this is a call to 17 -2 6060s. Just for all right, So they're full is called the situation as fight. So now if you absorb we have two equations four and five. So these are basically a system of equations in two variables. So we have successfully reduce the system of equations in three variables to two variables. So now we can go ahead and uh eliminate one of the variables preferably why? So that we can get is it directive? So let's do that. Yeah. Okay. So since we have to eliminate why from equation number four and equation number five, What we can do is we can multiply the equation number five x 6. So let me write the fourth equation as it is six. White Plus five. Is it Equals 130. And then I multiply the equation number five x 6. So every getting 618 to 6. White Plus five. Is that I'm sorry this should be six. Is it 6? Is that equals six times 4 is 24. So now as you can see that we simply have to add these regulations so that the why will get elevated? So if we add if you are we will not have to change the sign. So six by minus six is zero and five plus six. Is it is 11 is it? And here 130 plus 24 is 154. Now we divide by 11. So that we get is it? So is that equal 254 by No 1? Which means is that equal to 14? So we have finally founded the value of is that which means uh since is that a person a number of questions left attempted, so therefore we can say that number of questions left equals 40 so that's the correct answer for this question.

For this problem, it gives us that Obama's network is x amount of dollars. The mean um income or the network for all the presidents is some sort of number and then it gets its associated standard deviation right? So the first problem. First part of the problem ask us uh to find the difference between um Obama's income or Obama's network versus the income. The network of the mean of all the other patients, the President's. So for this problem we simply use of traction, so we just list Obama's net worth And then the mean of the sample of the presidents and you get some 1.26, million. So that's answer to part a for part B. You want to find the Z score for? Or sorry, not a Z score. But the actual how many standard deviations away the Obama's network is relative to the mean of the network of all presidents to do this. You take the difference between Obama's network and the mean network and you're divided by the standard deviation which is given in the problem. Right. And so from this you get that Obama Is .61 standard deviations away from the meat. Now, for part C it's asked us how many disease course is he away? Right. And so Z scores and the number of renovations away are the exact same thing except with a sign. Right? So you can intuitively tell that because Obama is below the mean. Obama must be negative .16 as the score. And we know that this is usual because um this sort of difference as usual because Obama's standard deviation From the mean is not -2 or plus two.


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