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Study finds that 75% of graduates attended a public college or university- 619 of graduates who attended 2 public college = or university graduated wlthln vears and...

Question

Study finds that 75% of graduates attended a public college or university- 619 of graduates who attended 2 public college = or university graduated wlthln vears and 6796 of graduates who attended non-E ~profit private collcgeE graduated within six years. pts) Create tree diagram tur the scenario above, What percent of graduates attended # public unlversity and graduated wlthin 6 years? What percent of graduates graduated wlthln slx years? What percent of those who graduated within six vears atte

study finds that 75% of graduates attended a public college or university- 619 of graduates who attended 2 public college = or university graduated wlthln vears and 6796 of graduates who attended non-E ~profit private collcgeE graduated within six years. pts) Create tree diagram tur the scenario above, What percent of graduates attended # public unlversity and graduated wlthin 6 years? What percent of graduates graduated wlthln slx years? What percent of those who graduated within six vears attended public college or university?



Answers

School Enrollment. The U.S. National Center for Education Statistics publishes information about school enrollment in Digest of Education Statistics. According to that document, $84.8 \%$ of students attend public schools, $23.0 \%$ of students attend college, and $17.7 \%$ of students attend public colleges. What percentage of students attend either public school or college?

For these questions. Wish you go about his act size. What he took to see how we used to treat diagram to help us understand the whole process. And here I give you this tree diver. But you can see the information in the screen. And our problem is to calculate the probability that a student who graduated from college in a 10 of public high school before So what we want is the conditional probability that the students attend a public school. Given that we know he was she's graduate, so use a conditional formula. We can cackle it as he ah from public school. I won't ask Pete and graduate, I was asked. Three. Divided by PG and the numerator we can see from the tree diagram is here from public school and graduate this site the probabilities They will 0.7 times their 0.75 derided by the probability graduate. Well, here we have to ah, to component off days Probability for the Graduate We can have these sides Ah, students from public school and graduate. We can also have day size student from no public school. Both graduate. So where's your ad? Is too component together, the probability equals to 0.7 times they will 0.75. Plus, There were points three times 0.9. Um, this approximately finally equals to the 0.66.

Okay. This question gives the proportion degrees that belong to minority students, and it asks us different probabilities in a sample of 10. So part a once, the probability of exactly two degrees in the sample belonging to a minority. So we just want the probability of exactly two of the 10 degrees belonging to a minority. So we can just use our formula where we have a sample of 10 degrees and we're choosing two of them to belong to minority students. And the rate of degrees belonging to minorities is 0.3 to 2. And that needs to happen twice, which means the rest of the time the degree is not going to belong to a minority, and that needs to happen the remaining eight times or to save work. You could just type this and your calculator as binomial pdf of 10 trials with a 0.3 to 2 success rate, and we want the number of successes to be to and both these will give you the same answer of 0.2083 then for Part B. It says three or fewer of the degrees belonged to a minority, and this can happen if we have zero of the degrees one degree to or three belonging to minority students. And we like this because this is a cumulative probability. This is the same thing as the probability is X being less than or equal to three. And we have a calculator command to find this. So this is cumulative binomial probability. With 10 trials, appoint 3 to 2 success rate and we want the probabilities of three or less, and this gives us the probability of 0.5902 Then for part C, it says exactly five do not belong to minority, so five do not belong to a minority and there's 10. That means that five must also belong to a minority because the remaining five have toe go to non minority students. So this is just another binomial pdf situation where we have 10 degrees choosing five of them to go to minority students with a success rate of 0.3 to 2. That has to happen five times, and then the remaining chance for it not so belonged on minority has to happen the remaining five times and again we could do this with binomial pdf the same as we did last time. Just this time we want five successes and set it to and this gives us 0.1 to 50 then. Lastly, Part D wants the probability with six or more. Do not belong to a minority. So six or more do not belong to a minority. That means we want the probability of four or less belonging to a minority because you could be there. 432 or one or zero. And as you can see here, this looks like what we did last time with the cumulative probability, because we can rewrite this one as the probability the X is less than or equal before which is just given by are cumulative function going up until probabilities for less, and this gives us a final result of eight 095

So we are using the Idea that 31.6% of people older than 25 have only a high school diploma. And we're taking a random sample of 100. And we know that if we take N times P and N times one minus P, both these are going to be greater than or equal to five. So this distribution is approximately normal, and the mean of that distribution will be N times P, which will be 31.6, and the standard deviation will be the square root of n times P, which is this 31.6 times one minus or the complement of this. And square rooted. And that gives us about. Let me look on my work here, four 649 for the standard deviation. So that's what we're going to use to calculate our Z values And we want to find what's the likelihood you randomly pick 100 people and you get exactly 32. Now we could use binomial calculations, but we want to use approximate normal calculations. So we need to use that continuity correction And we will think 32 and go a little happy unit below. So we're going to go to 31.5 And then we're going to go a half a unit higher and go up to 32.5. And we want to convert these both to Z value. So I'm going to write this one down and then the next ones I won't. So 31.5 minus the mean divided by the standard deviation and now that's the z value And then the 32.5 minus the mean, divided by the standard deviation, It's a nine right there. And we do that calculation, we get this z value to be negative .45 And we get this see value to be .84. And then I can look up this value on my table and find the area below and this value on my table and find the area below and find the difference between those two. And when I do I end up getting oh I apologize these values are not right. Let me just erase those This value. I'm looking at the next question. This was negative .02. And we raise both these. This was negative .02. I'm sorry I was doing the next part because I already did the work on this. And then look up this file, you find the area below, look up this value, find the area of the below. And when you subtract those two you get .0833. There we go. Now this is correct. Now part B. We're trying to find from 30 out of 100 all the way up to 35. And again we could find 30 31 32 33 34 35. And use our binomial calculations, but we want to use that continuity correction and so we need to bump this down, that's what we're going to use to calculate the Z. And we need to bump that up. Now, when I take this value right here and basically plop it right here in my calculator and to convert it to a Z value, I find that I get This z value is what I wrote down before, is the negative .45. Yeah. And again take this value and plop it in place of this value. Take to subtract the mean away and divided by the standard deviation. And we'll find out that this one comes out to be .8 for and then by the area below here, Find the area below here and subtract those two values and that gives us an area of .4732. And then our last one Is to find what's the likelihood of having more than or equal to greater than or equal to or at least 25 is the way I think it was worded. Now we need to bump that down to use the continuity correction. And so when I convert this to a Z value again, using that same calculation, this minus the 31.6, and then divided by the standard deviation of About 4.65. That gives me a Z value Of -1.53. And then instead of finding the area, instead of looking up negative 1.53 and finding this area, I actually looked up positive 1.53 and found the area below. So I didn't have to do this attraction. And that gives me a .9370. No, and I think we have all three parts.

According to the question, 3500 seniors were pulled for this example. We need to compare the number of seniors. That said academic reputation was the reason for their choice and the toe at the bottom of the graph in pink. We see the 630 seniors, so that document academic reputation was the reason for their choice. In order to find the percentage we need to divide 630 and 3500 things gives us a decimal of 0.18 We need to change this decimal to a percentage by multiplying times 100 giving US 18%. 18% of seniors said that academic reputation was the reason for their choice.


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