QuestionIn a sample of 832 people over the age of 30, 180 had high school diploma and 680 had high school diploma: Ifa person over the age of 30 i5 randomly selecte...

Apply Procedure 6.3 on page 289 to approximate the required binomial probabilities. High School Graduates. According to the document Current Population Suney, published by the U.S. Census Bureau, $31.6 \%$ of U.S. adults 25 years old or older have a high school degree as their highest educational level. If 100 such adults are seIected at random, determine the probability that the number who have a high school degree as their highest educational level is a. exactly 32 b. between 30 and $35,$ inclusive. c. at least 25

Hello, everyone and welcome were given this probability question. And let's write down what we know. We know that 1254 people. So it's total is equal to want to 54 We know that they were total women were 672 and of which, uh, 124 went on to grad school. So, grad women, what is equal toe? 124 then for men we have There are, um, 582 graduates. Oh, yes. 582 of which 198 went on to grad school. Yeah, So we want to calculate a few probabilities. Number one. We have to calculate the probability off. Female, male and female did not attend graduate high school. So quite a B and C. So the probability that they randomly select a female is the total number of females divided by the total number off graduates, which, as we should have a peer, is 1254. So we're essentially just doing 6. 72/12 54 which is 0.54 next for male. Um it is going to be the same thing. So how many males were there? How many men were there? 582. And how many total were there 12. 54. Therefore, this is equal 2.46 and we can confirm that this is correct, because when you add up these two probabilities, it adds up to 1.0, which is how should be in this case. So we can confirm that those air correct. Next, we want to see, um what are the probabilities that the person is female and did not attend graduate high school? Well, how many females did not attend Graduate High school? 670 to minus 124 which is equal to 548. Okay, so it will just be 548 divided by the total number of people which is equal to Oh, no, absolutely. Refresh the page. Well, im four party we had 548 divided by 12. 54 which is approximately equal to 0.44. So are the answers are 0.54 point 46 44. So thank you for watching. And I hope this helped

Alright. So in 47 we're giving some information about some young adults aged just 25 to 29. Um, from this information, we were told that the probability is 0.13 that the person did not complete high school. So no high school was 0.13 The probability of a high school Onley education is 0.29 and they were also given information about a group of people who has a bachelor's degree or more than that. So I'm gonna call that bachelors. Plus, that's 0.30 The first thing I noticed is that it's probably setting me up for a probability model here. Um and I am missing something because these numbers do not add up to 100% that is just gonna be considered other right now. So part A. We want to know what is the probability that someone has more than a high school education, but not quite the bachelors dot, dot dot That is the other that we're looking for. So because their probability model should have one as the total for probabilities or 100% I'm going to add up what I do, what I do have and that 72% subtract that value from one s 01 minus 10.7 to his point 28 That is my missing piece for probability. That is also the answer to A, which is 280.28 I knew that because probabilities and this probability models should some to one now and be The question is what is the probability that are randomly chosen? Young adult has a least a high school education. So I could do high school, other bachelors all combined. I can add those together or I could use this compliment rule one minus the probability of no high school whatsoever. So taking the the proportion of people who have no high school education, which is 0.13 subtract that from one get 10.87 So point at seven is the probability that a randomly selected young adult has at least a high school education. The rule was the compliment rule to solve that problem.

Okay, So for this problem were given this set of probabilities saying, for part A were asked what must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor's degree? So what? We're seeing some education beyond high school, and we're looking at the probabilities that were given. So we're given high school, but no diploma were given high school with a diploma, but no college or anything after that. And this one is you've completed college and beyond possibly so. The only probability missing here is the probability of having some college but not completing a master's degree. So remembering the rules of probability when we add up all of our probabilities, they have to equal to one. So whenever I take my probably some high school no diploma plus high school with a diploma, but nothing more plus my bachelor's degree or more, plus my probability of going to college, these all need to add upto one. Now I have everything here that I need, except for probably the college, but I could just solve out to Bradley for this. So whenever I combine like terms and subtract from both sides. Probability of going to college ends up equaling out 2.28 Now that's how we solve part. A part B asked. What is the probability that a randomly chosen young adult has at least a high school education? Now, if we're talking about at least a high school education, that means that they had completed high school. It doesn't matter if they went to college as long as they got their high school diploma. We're good to go. So we're looking at this probability, this probability and the probability that we just found the only one that we're leaving out is probably of high school, but not a diploma. So whenever I move this and started new page, when I move that over, we're gonna end up. All we have to do is add up those probabilities now. So we just found that are probability of going to college is a 0.28 We're gonna add that to our probability of graduating high school, but nothing more is 0.29 and the probability of at least a bachelor's degree, which is 0.3. You know, whenever I add all these up, this comes out to a 0.87 now. One other way to solve this. And this is the using arm Compliments rule. We can just take one our total probability and we can subtract this guy here. Me, this circle is in another code, and we can subtract this because we can say that Well, if the probability of getting not getting a diploma, the opposite of that would be the probability of getting anything else. So using that rule of compliments, we just take that and just subtract that probability. So we can say I mean changes back to purple. We have a one minus 10.13 and that also equals 0.87 Now you can do this, eat away, whichever one you prefer. Both of these will work, and that's how you solve it.

Hello students. So in this question we have been given three parts to solve. So we were going to solve this. So let us first tabulate the finding of the qualities away and I have already made that. So we in my pc and I'm just copying this. So this will be the table according to this will be going to answer who are first. The question is that let us try to find the probability that person selected at random is a female. So the total number of female in this survey is There's 6 75, 6 75. And the total sample size of the soviet is 1 21254. All right. So now we'll just calculate the probability. So it will come out to be 67657 are born 2254. It will come out Will be 1 21 30 when they dwell upon 209. So, the probability for the first part is this now coming on to the next part? The next part we have been asked to find the probability that a person selected at random is a male. So the total number of Total number of male. We have been given 5582. And the total sample size of the Soviet is when 254. Now we're going to find the probability which is p. e. equals two. There's 5 82 upon 125 ft. Which will be cut 97 upon 209 will be our probability. So now let us come on to the sea part. So let us try to we have been asked that let us try to find the probability that a person's electorate at a random is a female and I did not attend graduate school. So more females in the service is 6 72. And that's what a number of females who went to graduate as 124 food. So we will have to minus These 6 72. We'll have to minus this 124 from a total number. That is 6 72. So we'll get the uh we'll get the number of females who did not return the graduate school. So 6 72 -124, Which is equal to 548 flight. And the total The size of the Soviet is 1254. All right. So we'll calculate the probability which will come out to 2 74 ball 3 27. And this is your answer for the c. part. Thank you.