{14/2021Chapler 38 (34-3.5)- MTH 125, section 401SS, Sprng 2021 | WebAssign[-15 Points]DETAILSILLOWSKYINTROSTATI 3.Hw.113_MY NOTESPRACTICE ANOTHERprevious year; the...

In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data were compiled into the following table.
$$\begin{array}{|c|c|c|c|}\hline \text { Shirtt } & { \leq 210} & {211-250} & {251-290} & {>290} \\ \hline 1-3 & {21} & {5} & {0} & {0} \\ \hline 34-66 & {6} & {18} & {7} & {4} \\ \hline 66-99 & {6} & {12} & {22} & {5} \\ \hline\end{array}$$
For the following, suppose that you randomly select one player from the 49ers or Cowboys.
a. Find the probability that his shirt number is from 1 to 33.
b. Find the probability that he weighs at most 210 pounds.
c. Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210

Alright in this question were given that data about NFL players their years of experience in the columns, their weight categories in the rose and asked to calculate a bunch of probabilities Using the frequencies that are given. Remember the table You're given a joint frequencies right, represents a tally of players that meet those categories. We're going to take those numbers, divide them by our total and then get probabilities which will be numbers less than one. Okay, so always be paying attention to what kind of numbers you're using and what you're doing with them right now. Not all of the questions. All of the sub questions here are conditional. The first one is not it's a straightforward requests for probability. The questions if you choose randomly one of these 65 players, what is the probability that you will selected a rookie? Okay. So you want to know how many refuse total. So we're headed out here outside the box to the margin. Right? So in order to calculate the rookie mm probability the probability is that we have a rookie and we're gonna want to take all of the rookies. They're divided by the total. We'll have our handy dandy spreadsheet. Do that. Click on the 11 Divided by Our Killer 65. All right. And let's set this to have not too many decimal places. Right. There we go. That's better. four Decimal Places. There's plenty. Alright, the next question is About the weight. We want to know the probability that the weight is under 200. Right? Good. Less than 200. So that's again one simple category. Not a joint event. And so we want to go out to the margins right? To all of the players that way under 200 and take that number That eight divided by the total population of 65. Alright, so that's just straightforward kind of, you know, very it probability questions. Now, we start getting to the conditional probability questions. Okay, So now we're being asked what's the probability? Right? But you have a rookie but not out of all 65 players. We wanted to know what they're probably having a rookie Assuming or given that we're only considering players the way under 200. Right. Just looking at the category of those who weigh under 200. Right, so just looking at this category, what's the probability of getting a rookie? That's your column once earlier. That intersection of column 1? En route one. Okay, so um the nominator For this fact for this probability will no longer be 65. Because I'm not considering that I could draw from all the players, I'm only considering that I could draw from those in the lowest weight class, Which is the eight. And the number of rookies in that lowest weight class is just three. So this calculation is the three over the eight. Mhm. So in the next one, We've got ways under £2 or under £200.. Given I use a race, there's the same relationships. The numerator is going to be the same because I'm still looking at a player That's both under 200 and a rookie, so it's still going to use that three. But the denominator is different because now we are going to assume that we're looking at all the rookies, And I just want to know which one is under 200. Right? So that probability expression looks backward. I want to know if he's a lightweight, given that he's a first year player. Let's see how that a little backwards. We're writing up to symbols. Alright, so, again, someone looking column C. Because given that he's a rookie, so we're going to choose that joint event divided by the total of the rookies. Okay, so there's your probability for so into question E. It's just a matter of moving all those decimal places to to the right. All right. Watch what happens when you just click the button there, Right. And they just move that decimal places two places to the right and put the percent sign on. All right. So you can if they interpret expects sentences, you can say things like a third of all of the lowest weight class. Um, players, our first year players, that kind of comment that you can inmate or approximately Or be precisely say 37.5%. All right, that's all for this question. Hope you enjoyed it.

1 17 a previous year. The weights of the members of the San Francisco 40 Niners and the Palace have boys were published in the San Jose Mercury News. The factual data compiled into table 3.24 So we have a table of, ah, a bunch of information of shirt numbers versus the weights of players says for the following. Suppose you randomly select one player from the 40 Niners of the Cowboys. If having a shirt number from 1 to 33 waiting at most £210 were independent events than what should be true about the probability of a shirt being between one and 33 given of a player waste list? No. So what's being asked here is this. So we have Jersey Number went through 33 and the player weighing at most or, in other words, less than or equal to £210. The question is, are these two events independence? They want to know if they were truly independent. What should be true about the probability of a shirt being numbered one through 33 given that a player was at most £210. So what you'll find here is that these two things are truly and the shirt number and the weight of the player did not matter whatsoever. Then essentially, what would be true here is that this it would be the same exact answer as the probability of a player having a shirt number one through 33 regardless of their weight. So the red probability should be equal to the blue probability because knowing the weight of the player should not matter.

No one in question, one of one were given information. Similar games played for Chinese New Year in Vietnamese New Year. As it explains, the game's explains how the each game looks. It tells us how the rules of the game work were you better dollar and values. And the overall interest of this game is in the number of matches that you get in your game because that determines how much money you win. You get to a inwards to find the random variable X In this case, because X is gonna represent the number of Matthew's, we're just simply going to say X is the number of matches. The list of values that X may take on this game involves house role in three dice, and we're trying to determine the number of matches in the three dice. We could have zero matches, one match to match or all three matches so X could be any value 012 or three. See give the distribution of X because we can consider a match being a success and a non match being a failure. We have a set number, um, of roles here. We can say that X is about no meal distribution with N B and three, and the probability of a match is 16 D list. The vase that why may take on, then construct one pdf table that includes both X and why? And they're probabilities. Well, in this case, why is it being the profit per game? So why you could end up being a loss of $1 $1 $2 for $3 for the pdf table, I'm going to go to the side and created table in which the exes wise and the probabilities are all displayed. So form A pdf. I'm gonna write out my ex values, which was zero one, two and three. I'm also gonna write up my wife values, which were negative one one, 23 because both my ex and my wife values had the same probabilities instead of writing p of X appeal. Why? I'm just simply gonna right crop, as in probability, indicating that's the same probability for either the X or the why and the probabilities for each of these events. The probability, the X zero or that why is negative one ends of Ian 0.5 seven. So and I got this value because we do have a binomial distribution as we figured out in court. See, because we have a binomial distribution calculated this value using the information, find me a pdf in which I had a total of three rolls, the probability of 16 and upload in zero as my ex by you, this gave me 0.5787 I used the same approach with 12 and three to fill in the rest of my table. Because I do this, I get 0.3472 get 0.6 94 0.46 This creates a PdF table for both maxes and wives with their probabilities. E calculate the average expected matches over the long run of playing this game for the player because it's asking about the number of matches. I'm looking at the X values here, so I'm gonna use the formula in Times P. There's three total rolls. Probability is 16 So I would expect 0.5 matches calculate the average expected earnings over the long run playing this game with a player. In order to do this, we're gonna figure out our average winnings for why, which is calculated by the summation of taking every single why value and multiplying by the probability of his wife values. In this case, we have negative one. Multiply about probability 0.5787 We're gonna add this to the next Y value, which is one in its probability. 10.34 72 plus next, wise to times of ability 0.694 then what are added to three times point 00 for six. All this gives you an expected earnings to be negative 0.8 Or you would expect to lose about eight cents of the long run per player. G determine who has the advantage, the player or the house. The house has the advantage big time in this case because the expected winnings for the player would be negative. So House expected winnings for the player negative. That indicates that the house is making some money

So if the reality is true that the main weight of man Is 188 .6 lbs. With a standard deviation of £38.9.. And in part a they asked, well what's the likelihood that I randomly chosen male will weigh less than 100 and £74. And let's convert that to A Z. We have 174 -188.6, Divided by the 38.9 and left parentheses. E. 1 74 minus 1 88.6. Close my parenthesis E and then 38.9. And when I type that in I find that that gives me a Z value of negative .375 32 etcetera. And if we were looking this up in a table we would probably go to negative 0.38 and look that value up. I'm going to use software, my normal CDF button so I'm going to have a negative Say 1000 be my low limit. And then I'm going to for my upper use this value. And so it hits second in that button And I'll leave the mean and standard deviation and 01, respectively. So when I do that, I get that probability is .35 3 7. So about 35 chance of randomly choosing a male and be weighing less than £174.. Now, part B says if we assume that the mean was what missiles for males? If we assume that the main weight of a person on that, including males and females, and if the boat has a limit of £3500,, how many people we say we can get on there? And so if we divide, it looks like we can get 25 people on the boat. If their averages 140. On the other hand, if it were have your people or all males with this mean, and we divide, look how it is significantly less People. It comes out to 18.55, which I would say, let's round down and so we can only have 18 people Because if we round up, then you're gonna have to wait more than 3500 with that average. So there's a significant difference. So we definitely need to look at and review this. We need to review regularly to look at what the mean. Wait. Also, they may want to do some type of a look at gender and see which gender comes or just find some weights that are average and look at males and females about how many people get on the on the boat and so on. To make a judgment as to what that means would end up being.