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The following cross table represents the type and number of employees in 2 points some Palestinian schools. If a school is private, What is the probability that it ...

Question

The following cross table represents the type and number of employees in 2 points some Palestinian schools. If a school is private, What is the probability that it has 30 to 39 employees?# of employees Private Governmental Total10 19 20 29 30 39 40 49 50 59 Total3 10 2 1812 158 5032

The following cross table represents the type and number of employees in 2 points some Palestinian schools. If a school is private, What is the probability that it has 30 to 39 employees? # of employees Private Governmental Total 10 19 20 29 30 39 40 49 50 59 Total 3 10 2 18 12 15 8 50 32



Answers

Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Comfortable Retirement Fifty-one percent of workers are confident that they will retire with a comfortable lifestyle. You randomly select 10 workers. Find the probability that the number of workers who are confident that they will retire with a comfortable lifestyle is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.

Alright, This problem is a binomial probability and we know it's a binomial probability because it meets certain conditions and the conditions it needs to meet are one it needs to have a fixed number of trials. Second thing is each of the trials must be independent of each other, and the third thing that has to be holding true for a binomial probability is that there's only two outcomes, and we define those outcomes as success and failure. Now, when we're doing binomial probabilities, there's a couple different variables involved, and the variables are n which is the number of Trials X, which are all the possible outcomes key, which is the probability of success. And Q, which is the probability of failure. And keep in mind the probability of success and the probability of failure should add up to one. So going through this problem, let's see that we've met these conditions before we solve it. All right. So as we read through this problem, we find that there is a fixed number of trials in this case, and it's six, and we were asking the people whether they felt that the government should fight childhood obesity and we only asked six different people. The values for X could be that zero of the people believed that the government should fight obesity or one of them or two of them, or three or four or five or six. And we found in this survey that 39% felt that, yes, we should be having the government fight childhood obesity. So that means P would be 0.39 and then Q would be the other 61% that said no, they didn't believe that. Now, when we're solving uh, binomial probabilities, the formula that is necessary is that p of X equals the combination, and C x multiplied by p, raised to the X value multiplied que raised to the n minus X value. So the easiest way to handle this is to put our data into the calculator and let the calculator do a lot of the work for us. So before we try to answer Parts A, B and C, let's add the information to our calculator. So I'm gonna bring in my calculator, and I'm going to select the stat feature, and I'm going to edit that we can fill in the information in our list and enlist one. We're going to put all of the X values, so we're gonna put in zero and one to three, four, five or six. So those were the only possible outcomes. If you're talking to six people, zero them could believe it or all the way up to six people can believe. Yes, we need to have the government fight childhood obesity. Now that we have done that, we need to find the probabilities for each one. So we need to put all of these values into the formula. So we need to put the zero in for the exes. We need to put the six in for the end. We need to put the 0.39 in for the P and the 0.61 in for the Q. And we've got to do that for the one and for the two and so forth. So the fast way of approaching that again is to go back to your graphing calculator. So if you sit on top of the l two, we can generate a formula, and instead of us saying, N c X, what we're going to do is end with six and we have stored all our exes. Enlist one. So we're going to type that in. Then we're gonna multiply it by 3.39 And all of our exes were again stored in list one. And then we're going to multiply it by the 0.61 and we're going to raise that to the sixth minus X will again. All of our exes were stored in list one. So when I do that, I'm going to type in six. I'm gonna go and grab the, um, probability, and it doesn't want to let me get that.

Now this problem is about asking adults whether they think the government should help fight childhood obesity. And it falls into the binomial probability category because it meets certain conditions. There are going to be a fixed number of trials. The trials are going to be independent of each other, and there's only two outcomes, either success or failure. So as we read through this, it said that 39% of U. S adults think that the government should help fight childhood obesity and you randomly select us six US adults. So there's are fixed number of trials, so N is going to be six. And when you ask one adult, um, the next adult is not going. Their answer is not going to be dependent on the previous one. So the trials are independent. And are there only two outcomes? Yes, either. Yes, they believe the government should help fight childhood obesity or no, they should not. So with binomial probabilities, we have a number of variables, one of them being and the other one is going to be X, which is all the possible outcomes. And if we talked to six different people, zero of them might believe that the government should help fight childhood obesity. Or maybe one of them does. Or two or three or four or five or six. There are two more variables associated with binomial probabilities, and that's going to be the P and the queue and P is the probability of success when you reach out to these people. Um, what's the probability of finding someone that believes the government should help fight the childhood obesity? And since it said 39% of U. S. Adults think that way, then our P is 0.39 Now, cue is the probability of failure. So if 39% of the population believe, yes, we should have the government intervene with fighting childhood obesity, then that means there's 61% that don't believe the government should intervene. And when it comes time to do binomial probabilities, we're going to apply this formula. The probability off an event happening is equal to N. C X multiplied by P to the X power multiplied by Q to the n minus X power. So we're going to take all that information and we're going to apply the formula Thio answer three parts to this question, and in doing so, it's possibly or probably best to set up a whole binomial distribution. So we're going to set up a chart, and then we're gonna answer the questions. So the first column of the chart is going to be all of the different possible outcomes. And then the second part is going to be each of the probabilities. So the first go round to find the probability of zero. We would put a zero in where the X is in three different places and we would put the 0.39 in where the P is on the 0.61 in where the Q is. And we would put a total of six everywhere there's an end, and then we would go back and we would alter that formula with X being one. And then we alter the formula with X being too and so forth. So this is where we are at the moment. So we have six see X multiplied by the P value in this instance is 0.39 raised to the X power multiplied by 61.61 raised to the end minus X power and the end in this case is going to be six minus X power. Now again, the X keeps changing. So the easiest way to fill in the entire probability distribution is to utilize your graphing calculator. So I'm going to bring in the graphing calculator. And if you hit stat and edit and you put in your numbers zero through six and then if you go and sit on top of the l two column and type in six, access your combination under Math Probability and C r. And then all of our exes, we have housed Enlist one. So we're going to tell the calculator toe look, enlist one for every one of those exes. We're then going to multiply that by 0.39 raised to the X power. And again, all of our exes are enlist one. And then we're going to multiply that by 61 raised to the power of six minus the accent again. L one holds all of our X values, and when we hit enter, it's going to fill in the entire chart. So I'm going to come back to our chart and I'm gonna fill in what you see in the graphing calculator. So it's 0.0 515 to 04 and then we see 0.197 6355 Then we see 0.3158 9 to 9. And for three we see 30.2692 857 and for four 0.1 to 9 1247 and the probability of five this 50.0 33 02 to 1. And for six, the probability ISS 60.0 35187 So that's our probability distribution for n being six under these circumstances. So now let's look at the actual problems. Part a part A is asking you to find the probability of exactly two people out of these six believing that the government should get involved with childhood obesity. So we're just gonna look in our chart. We're gonna take the value, So the answer is approximately 3159 for Part B. It's asking us what's the probability that the answer or the number of people is greater than or equal to four. So if that's the case, you're going to take the probabilities for 45 and six and add them together. And when you do that, you should get 0.165 seven ish and for part, see, it's asking you for less than three. So for part C, we want the probability that X is less than three. So in this case, less than three would be 01 and two. So we're going to add those three probabilities together, and you're going to get approximately 0.565 So therefore, our answers to this problem are right here. Probability that there's exactly two out of six is 0.3159 Probability of at least four well, at least four is greater than or equal to four would be 40.1657 and the probability of less than three would be 30.565

In this case was simply need to find the probability off the age group 20 to 30 adore so that is 20 to 30 years old. So from the table which is given live, discount out all cases which is from 20 to 30 years old. So the number of people into this event this see, so a number of eliminate that even see is equivalent to 20 to 30 which means age group off printed 21. We will be found in this case plus number of people which are in the age group of 20 to 30. Okay, so when people can't even there, a couple of 18 people's on 22 to 30. There are called love to people's, so that is equivalent to 20. The number of element in the sample space is 32 okay. And study quite probabilities equals two 20 or what to do, which is spent over 16 or which is equal to five for it. All right,

All right. So you students the sample 20 students have been taken out of five. In which those 20 example off Those vegetarians, they say 19 efficiency. Three. Any fish. So she's over. This promises those fish, and this is a Well, where would you intersect? Will be? Nine. Which fish? And let's see, we have three that he pays with a fish. And you have eight. Neither of these three numbers they should add to your total 20 minutes hearing. So we don't have a scenario where they just fish and not me. This you've got a total of 20 material. They want what is probably the troubles in student Rob the vegetarian, right? So we're talking about our role of our sample, which is our vegetarian number of Syrians. Guys do not either. So you guys carrying those 40 vegetarians age


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