A recent report on American children under 8 years of age suggests that 56% of children believe in Santa Claus, 64% believe in monsters, and 40% believe in both:(Hi...

Psychology: Myers-Briggs Approximately $75 \%$ of all marketing personnel are extroverts, whereas about $60 \%$ of all computer programmers are introverts (Source: A Guide to the Development and Use of the Myers-Briggs Type Indicator, by Myers and McCaulley). (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 5 computer programmers, what is the probability that none are introverts? What is the probability that 3 or more are introverts? What is the probability that all are introverts?

In this problem, we have to answer the cautious asked using the given circle graph. The first question asked this to estimating a butt off idols who give us public schools a B. It can be seen from the G. What's Alka graph that deposed some of the girls will give us public schools are B is frank before your son. So you experiencing a lot of adults who give B We take this drink before we are a very brave in bold print person. Just 100 and multiplied by the population. Off the adults. We'll give a grid. It is given dead. What, 1011. I don't but after grid Oh, this is a would do frank before counts on 264 divided by hungry. This is a quite do who thought we do by 64 bridges Approximately will do through 43 but this through for victory. Adults gave us public schools off B. Now the next question asked is to find people probability right? But I don't select at random will give the U. S. Public schools and A it can be seen from the given circle graph. That group will sink. I don't gave us schools and a so to find they require probably deep. We take this school nearby writing Total Person We chris 100. So this is it went toe one divided by 50 Britain's hour required. Probably now the next Russian asked is to find the probability that I don't selected at random will give the U. S public schools off c r A d and so we can see in Vicky. What sample graph the number sent off. Girls who came US public school say see crisp repeat group on Sunday. This mean for center for girls Who will give you rest? Probably schools or B is 12% resisted some off sense off I does will give us public schools are see already This is it will do 64. So to find a great probability reaping the 64 we righted Ready hotel person with this 100 so 64 divided by 100 this is equal toe 16 divided right. Bring any friends bridges over the quiet probability

All right, this question asks us about a binomial experiment with 15 trials and a probability of success of 150.28 So part eh asks for the probability that there exactly four successes and that just plugging into the binomial distribution formula you get 15. Choose for times 0.28 to the number of successes times probability of failure to the remaining number of trials, which is the same thing as saying, If you have a T 84 by a no meal, pdf pdf because we're only interested in one probability 15 trials 0.28 success rate and we're interested in X equals four. And both of those answers work out 2.2261 All right, And then Part B asks for the probability the X is greater than or equal to three, which equals one minus the probabilities. We don't want soapy zero plus p one plus p too, which can be written as one minus the key mood of probability. So Bynum CDF 15 trials 150.28 probably of success, and we're adding all the probabilities upto X equals two, and that works out to 0.835 five

Right. This problem is about junk food and how us adults think about special taxes on junk food and soda, and this problem will fall into the binomial probability category. And just to review what a binomial probability consists of, we've got to have a fixed number of trials. Each trial has to be independent, and there are only two outcomes. Success and failure. And when you're doing binomial probabilities, there are four variables that come into play. We've got the variable N, which represents the number of Trials X, which are the possible outcomes of the Event P, which is representing the probability of success and cue, which represents the probability of failure. And lastly, as an overview of a binomial probability. In order to determine probabilities, you're going to use the formula P X equals and C X multiplied by P to the X power multiplied by Q to the n minus X. So let's go through this problem and identify the different variables. So it's saying that 63% of U. S adults opposed special taxes on junk food and soda, so that information is giving us a value for P. So we have 63% now, even though they don't come out and tell you the probability of failure. If 63% believe or are opposed to these special taxes on junk food, that means that there are an additional 30% sorry, 37% out there that are not so therefore Q. With equal 0.37 and you are going to randomly select 10 U. S. Adults. So that means N is going to be 10 and X could take on the value of zero or one or two all the way up to and including tent. So that's saying Nope. Of the 10 people we select, no one is opposed to those taxes or one person is opposed or all the way up to 10. So for part a of this problem, it is asking you to determine the probability that exactly six of the 10 selected adults are opposed to special taxes. So using the formula, it will be n which is 10 c x, which in this case is six. We're going to multiply it by the 0.63 which is RPI value raised to the X power in this case, X is sex and then we're going to multiply by 0.37 raised to the 10 minus six power. And when we do that math using our calculator, you're going to get in approximate value of 0.2461 in order to solve Parts B and C. It's best if we look at the entire probability distribution. So for parts B through parts B, N. C, we're going to construct a probability distribution and probability distribution is just a two column chart listing all of our potential X values and then listing all of the probabilities associated with that. So now, in order to do that instead of us having to use the formula that we used in part a 11 different times, what we're gonna do is we're going to utilize our calculator, and when we put it into our calculator, we're going to do 10 c x, because X is going to change. And then we're gonna multiply that by six three toothy X power again. That's going to change, and we're going to multiply that by 0.37 raised to the 10 minus X power. In order to let the calculator do that, we're going to have to use the stat feature. So I'm gonna bring in my graphing calculator and I'm going to clear out what was in there from a previous problem. And I'm going to put the zero through 10 into list one and to let the calculator efficiently give us all these probabilities. We're going to sit up on top of the l two, so notice where I've put the highlight up on top, and I'm going to type in the formula that I generated right here. So I'm going to do 10 now to access your combination. You're gonna hit your math button and the probability tab, and we've got our n c r and then our ex. Well, since our X keeps changing from a zero to a one to a two to a three and all of those exes air found, enlist one. I'm going to hit the second button and list one. I'm then going to multiply that by the 0.63 raised to and instead of typing in X since all of our exes Aaron list one, I'm gonna put list one, they're a swell, and then I'm going to multiply it by the Q, which in this case is 0.37 raised to and this time I'm going to do 10 minus list one. When I hit enter, it's going to give me values for all of the probabilities. Now, keep in mind when you see something in scientific notation the negative past E is representing the movement of the decimal point in this case, five places to the left. So we're going to have a value of point 0000 48 086 as the probability that none of the 10 people are opposed to the junk food tax for one person, we're going to move the decimal place four places to the left and get 40.81876 for two 0.62735 and you can copy as I go as well. Then we're gonna do four and five and six. The probability that seven people and then probability for eight and for nine, and finally the probability for 10. Okay, so I'm gonna take the calculator out of the way. And now we're going to answer part B and part C in part B. It is asking you What is the probability that at least five of the 10 U. S. Adults are opposed to the special tax? So at least five translates into X is greater than or equal to five. So at that point where you're going to have to add up, the probabilities for X is greater than or equal to five. And when we do that, we get a probability of about 87 95 And then for part C, it is asking you what is the probability that less than eight of the 10 U. S. Adults are opposed to this special tax? So we want the probability that X is less than eight. Well, the numbers here that are less than eight would be 76 all the way down to zero. So in this case, we're adding up all of these probabilities, And when you add those up, you will get approximately 0.7794 So just to summarize the three answers to this question, we've got the probability that X equals six as 0.2461 The probability of being greater than or equal to five is 0.8795 and the probability that X is less than eight is 0.7794

Ocean here basically states that we know that 58% of American Children are to read every day by someone at home our right to brother every day by someone at home. So if we have a group of five Children that are randomly selected, what is the probably that at least one is read to everyday by someone at home. So in order to find this as easy as possible, we first of all need to find the probability that they're not read too, which is going to be 48% or one minus 50% here, or is your 500.48 and then to find the probably that at least one is ready to buy someone every day. We need to find the probability, first of all, that they are not read to within this subset as their five people. We put this to the power five as the probably that every single Children here are not read too. Is, um, this probably or 48% here multiplied five times as we're taking five different Children. So to find probably at least one is ready every day. We basically need to take one minus that? Probably that none of these Children are red, too every day. And that is going to give us this answer here. So this is going to be the formal for this question here.