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In an elementary school there are 25 teachers and 5administrators. A group of 12 is to be selected to participate inan educational workshop.What is the probability ...

Question

In an elementary school there are 25 teachers and 5administrators. A group of 12 is to be selected to participate inan educational workshop.What is the probability of having exactly 8 teachers in thegroup? (Round your answer to the nearest thousandth).What is the probability of having no administrators in thegroup? (Round your answer to the nearest thousandth).

In an elementary school there are 25 teachers and 5 administrators. A group of 12 is to be selected to participate in an educational workshop. What is the probability of having exactly 8 teachers in the group? (Round your answer to the nearest thousandth). What is the probability of having no administrators in the group? (Round your answer to the nearest thousandth).



Answers

Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Jessica is one of eight kindergarten teachers at Mandela Elementary School. One of the kindergarten teachers will be selected at random to attend a summer workshop. Find the probability that Jessica will be selected.

To find the probability of that event, we take the number of favorable outcomes in divided by the total number of outcomes. So to find the probability that Dane is the one chosen to bring the doughnuts, we find the number of favorable outcomes, which would be one because there's only one Dane divided by the total number of outcomes, which is 24 because they're 24 people to choose from. So that's the probability 1 24th expressed as a fraction. And to express that as a decimal, you take one and divided by 24. And that one does not terminate. So we're gonna round it to the nearest 1000th. We're going around 23 decimal places and we get approximately 230.0 for two.

To find the probability of an event. We take the number of favorable outcomes and divided by the total number of outcomes. So in this problem, we're finding the probability that Donovan visits an out of state college if you randomly selects from 10 out of state colleges and foreign state colleges. So the number of favorable outcomes would be 10 because he has 10 out of state colleges on his list and the total number of outcomes would be 14. Because there are 14 colleges on his list altogether. Let's reduce that fraction, and we get 5/7 and that's the probability that he will visit and out of state college. And then we can convert that to a decimal. We're going to have to round it to three decimal places, and we get 30.714 as the probability of visiting and out of state college

This is a problem that's going to require us to use the normal CDF function from a calculator. So if you have a graphing calculator, a calculator with that ability and great, if not remember you can find them on line. If you just go to Google, type in online calculator with normal CDF function, that will probably all you need to type in to be able to find one that works. But whether your uncle clear whether online you will need something that can do that for you. So you deposits video quick and go find that. Go ahead and do that. If we're gonna be using the normal CDF function from our calculator, there are four things we're gonna need or ended a low Ah, high. We're gonna need a mean and a standard deviation low in the high are going to be found from whatever we're being asked from the information given in the problem, the mean and the standard deviation are something that we're gonna have to find ourselves based off the n and the P that the problem will give us the number of trials and a probability of success. All right, let's start with low in the high cause. That'll be the quickest one to figure out. We're being asked, What is the probability that the win, at least 12 out of 25 games, at least 12 name 12 is the lowest amount of games acceptable? Now we are estimating here, using the normal approximation. So rather than use 12 as are low, we're going to use 11.5. It does say at least 12. 12 is the lowest we're supposed to accessible. We're gonna allow for a little bit of wiggle room here, since we're having to estimate. Okay, so then the question is, what is our high? Well, the high would be the most amount of games that we can possibly win. We're only playing 25 games, so can't really win more games than you play. We'll make it 25.5 again to allow a little bit of wiggle room because we're estimating. But we can't go any higher than that right now, as far as the mean and the standard deviation. Those we need to actually find ourselves based on what N and P happened to be en, is supposed to be the total number of trials in this case again, we already said We're playing 25 games. So 25 is the number of trials. P is the probability of success on any given trial in any given game. And it specifically tells us this problem is pretty nice cause it's straight up. Just tells us the probability that they'll win any even Game 0.5. So we didn't really gonna have to do too much looking there. It just gives us those Okay, so for the mean, then we find our mean by taking end Times P, which in this case would be 25 times 0.5, 25 times 0.5, were essentially 25. Divided by two would be color change 12 0.5. So we have a mean of 12.5. All right, standard deviation is the last thing we need to solve for, so that is the square root of end Times P, which we've already figured out that in times P is 12.5, so don't willing to do that again. And then the quantity of one minus p so one minus 0.5 well, one minus 10.5 would just be 0.5. So where you taking the square root of 12.5? Time 0.5? A lot of repeated point fives there, I will say so if you take 12.5 times 0.5, you get 6.25 and if you square root that it looks like you should get to 0.5, so are mean is 12.5, but our standard deviation is 2.5. So again, now is the time to go to your calculator, whether it's your own calculator, whether it's when you're using online. But I got a low of 11.5. You have a high of 25.5, a mean of 12.5 and a standard deviation of 2.5. Plug all that in, as always, feel free. Deposit this video if you want. Take time. Make sure you get that plugged in once you've plucked it in. What you should get is 0.6 554 We were asked around three decimals, so that would be approximately 0.655

To find the probability of an event. We take the number of favorable outcomes and divided by the total number of outcomes. So in this problem, we're finding the probability that Noah randomly selects a beach campground instead of a, um, mountain campground. So the number of favorable outcomes would be six because there are six speech campgrounds and the total number of outcomes would be 18 because they're 18 campgrounds all together. So we can reduce this fraction and we get 1/3. And that's the probability that he will choose a beach campground and then we can convert it to a decimal, and we get 0.333 is the probability.


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