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Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
$$\begin{array}{|c|c|c|c|c|c|c|}\hline 1.5 & {2.4} & {3.6} & {2.6} & {1.6} & {2.4} & {2.0} \\ \hline 3.5 & {2.5} & {1.8} & {2.4} & {2.5} & {3.5} & {4.0} \\ \hline 2.6 & {1.6} & {2.2} & {1.8} & {3.8} & {2.5} & {1.5} \\\hline {2.8}&{1.8} &{4.5}&{1.9} &{1.9}& {3.1}& {1.6}\\\hline\end{array}$$
$$\text{Table 5.4}$$
The sample mean $=2.50$ and the sample standard deviation $=0.8302.$
The distribution can be written as $X \sim U(1.5,4.5).$
What is the $90^{\text { th }}$ percentile of square footage for homes?

To solve this problem. We're going to take all the given information and put it into a Venn diagram, and then we can go through parts A through eat. So we're going to start at the bottom of the list, which is actually over here. There are five people in the survey who had shares in all three kinds of stock. So the five goes in the part that overlaps all three circles now, working our way back up. We have 20 people who had IBM and A T and T, And so in the section that has IBM and A T and T, we need a 20. When we add these two together, we already have a five. So this is a 15. Kate, check that one off the list. We have 15 who had A T and T and G E. So a t and T N G would be this little portion here, 15 altogether. We already have a five, so the next part would be 10. We have 20 who have IBM and GE. So that would be this little part over here. 20 and there we already have five sort of 15 more. Okay, we're working our way through. Now let's complete the G E Circle. So in G either supposed to be 45 altogether and we see that we already have 15 5 and 10 so we already have 30 so we need 15 more. Let's complete the A T and T Circle were supposed to have 40 altogether, and we already have 15 and five and 10 and that's 30. So we need 10 more. Let's complete the IBM Circle were supposed to have 50 all together, and we already have 15 and 15 and five. So if 35 so we need 15 more. Now let's add all these numbers together because we know that they're supposed to be 100 total. That will tell us what falls outside. So when we have these together we have 15 and 15 and 15 and five and 10 and 10 and 15. That's 85. So on the outside, we're gonna have a 15. So how Maney had no shares in any of these, that would be 15. That's our answer for part A. Now we go under Part B. How many had just IBM? Let's look at the IBM circle and just the part that doesn't overlap with anything. And we have a 15 part See how many have just g e? Look at the G E circle and the part that doesn't overlap with anything. And we have 15 there as well. Okay, for part D, we're looking for the number of people that had neither IBM nor G. E. So that would be the numbers that are not in those circles. So we have a 10 for the A, T and T, and we have a 15 on the outside. So that would be 25. And lastly for party. We want to know how many people had IBM or a T and T, but not G. Okay, so we have all the numbers that Aaron IBM or they're an AT and T, but they're not in G e. So that would be 15 and 15 and 15. Oops, Let's go back a little bit. Get rid of that one because that one had g e. So we want the ones that don't have G. So we have 15 and 15 and 10 IBM or A T and T. But not G. I bet. I guess that's it. So that would be 40

So we're given a lot of information for this problem that we're expected to use and to help simplify some things. We're just going to start assigning variables to certain parts of the problem. So we're gonna have that. We bring a sign eight IBM eat A, T and T and C to G. So we know that a is equal to 50. We know that B is equal to 40 and C is equal to 45. We're also aware that, um, a intercept see is equal to 20 were given that be intersect to see is equal to 15. And we're also given that, um, a intersected Buz go to 20 as well. B is equal to 20 and that a Intersect to be intersect C is equal to five and are expected to come up with a lot of information for this. So for the first part, we're trying to find out how many of the 100 investors are not represented in the state of given. And to do that, we are trying to find out how many are represented. That's an easier way to think of it. So we're trying to find out a union be Union seat, and then we can take 100 minus this number, and I will represent everyone who's not there because we know the A union. Be union. See, there's equal to three elements added together minus the separate intersections. So a plus B plus C minus a Intersect B minus a intercept C minus Peter sexy and then plus the intersection. So plus a intersects b intersect See, and the nice part of writing things out in more in terms of unions. Intersections, as seen above is that when we write an equation like this, we can know what we have to find if we're going to use this equation and in this equate a case, we actually already have all the numbers for this equation so we can just start plugging you. Just cause is that a union be union, see is equal to 50 plus 40 plus 45 minus 20 minus 20 minus 15 plus five, and this is going to be equal to 80 fun. So 85 investors are represented or 85 investors did invest in IBM, A, T and T and G, and that tells us that since there's 100 investors total that 15 of them 100 minus 85. 15 of them do not have any representation in those three companies, any stocks. The next thing we're asked to find is how Maney own just shares in IBM. So to calculates the people who only have shares an IBM, we can take the We'll call that because our eggs, that's all right. A variable we can take a Let me just write that black so you can take a minus the intersections. So a intersect be plus a intersex seat, uh, minus a intersex t and her sexy. And so this will be equal to a which is able to 50 50 minus 20 plus 20 minus five or 35. So 50 minus 35 is equal to 15. So there are 15 people you have just IBM shares. And then we knew the same thing for the next couple parts of how many people own Justin G E shares and that would be equal to e minus to be intersex. So a intersex be plus e intersex see minus a intersex. Be intersects, See. And in this case, let me just referenced my numbers really quick B is 45. No, sorry. This is an error on my side. G is very well. See, not very will be. So I'm just going to rewrite this really quick. This would be how you were doing if you were trying to find a T and T, though just the problem does not ask for, um, certain parts in the order of Gibson. So this will be C minus a intersex C plus B intersex e minus air said to be intercepted. See, So C is 45 minus a intersex See plus B intersex C minus. Anderson to be in her sexy, which is going to be 20 plus 15 minus five. So 45 minus 30. And that's equal to 15 quite suddenly as well. So 15 investors do not have any stuck. 15 investors own just IBM and 15 investors own G e The next for us to find out how many of the investors own neither IBM or G. So to do this, we want to find out every investor who does own idea and G and we can do this by taking a plus. C. We're taking a policy minus the intersection of the two. So a intersection see? And this is equal to 50 plus 45 minus the intersection of IBM and GE, which is 20. What this does is that 75 people have stocks in IBM or G, so that people who have no stocks tonight the energy would be 100 minus that number or, in this case, 25 and then for the final part. When you're asked to fight, we're trying to find how many people own IBM or a T and T, But no G. And so to calculate this, we're gonna do the same thing of IBM and G on together. So a plus B minus the intersection of the two. So this is how many people own IBM or a T and T so eyes of a Intersect beat. And this is going to be equal to 50 plus 40 plus a Intersect B, which is 23 minus Anderson. To be 20 that's able to 70. So 70 people own Ah, IBM or A T and T. But now we need to find out how many people own G that are a part of the people of IBM, Maury, TNT, and to do this. We're just going Teoh, use the same formula earlier where we're going to take this number 70 subtracted by the A intersex C plus a b inter sexy. So they intersect. See, plus B inner sexy minus the total. In your section. People have socks and everything, so a intersect be inter sexy. This is going to be 70 minus a Intersect C, which is 20 plus b intersect. See, which is 15 my ass and I was like to be intersex C, which is 5 70 minus 30 or 40. So to quickly recap, there are 15 people who have no stocks in any of three companies. 15 with stocks in just IBM and 15 with stocks in just g e. Just quickly reference we have ahead. Yep. And then there are 25 who have neither IBM or G and 40 who of IBM or agency. But nog

So when, um, talking about personality according to the research, genetic factors account for around 12- 25% in two B. A personality, although right genetics does have an influence on personality. Yeah, the environment wanted and or was raising Please in we're a major role and influencing personality.

Okay, so for this question, the first part was going to solve. He is the number of my employment. So we know that employment rates are defined by number of employment divided by the amount of labor force. So we see that the amount of the person they shall by employment is 5.3%. So that means on the employment ratio. So the employment rate is 94.7% to that is employment racial. So if we use the amount of employment, that is all 148739 and triple zero divided by 94.7%. So this number is exactly the amount of legal force in this market. So if you do this calculation, believer force in the markets actually closed to all one for eight censoring 9000 divided by nine 4.7% to that close to 157 063 and, uh, three eights. Okay, so that's amount of labor force, and, um, so we can fill in this blank here, and the other one is the unemployment rates. So you on Chicago would see among the by appointment a single use I'm not a label horse, minus the amount of employment. We have the amount of labor force to be this 157 something. And your mother employment is one for eight something so you could get off the amount off my employment there. Okay, so we have feeling onto once and help honor, too. So of the employment population ratio ISS oh, legal force participation rate till the labor force participation rate is basically on the among the label force that is actually use core the amount of labor force that is that it's used needles, working age, population. So we know that the amount of labor force is this'll one thug, seven something. So we need to divide it by the label worth where that is. 6 to 7 60 Just 2%. Last waiting here. Hey, Holly gets on the working age population that is equal to amount of label horse. They wired by labor force participation rate it is 62.6%. So if you do, this calculation actually goes to quiet. Zil 0899 Nice horse race. And then you have a feeling this fly here. Working age, population and the last one is employment population ritual that is calculated by the amount of employment that is 14 So this little our last one, let's see employment population. Your show that close to the amount of employment, your model in accordance delighted by the amount of working age population. So that's the way how you got this blank showing your doo miscalculation. You're actually supposed to fly 9.3% and that's the way how you get this result.