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Question2 pts(CO 4) Consider the following tableAge GroupFrequency18-2998330-3978440-4968650-5963260-6954170 and over527If you created the probability distribution ...

Question

Question2 pts(CO 4) Consider the following tableAge GroupFrequency18-2998330-3978440-4968650-5963260-6954170 and over527If you created the probability distribution for these data, what would be the probability of 80- 3920.1300.1270.1570.165

Question 2 pts (CO 4) Consider the following table Age Group Frequency 18-29 983 30-39 784 40-49 686 50-59 632 60-69 541 70 and over 527 If you created the probability distribution for these data, what would be the probability of 80- 392 0.130 0.127 0.157 0.165



Answers

Consider the following table of ages of U.S. senators:
$$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Age (yr): } & <40 & 40-49 & 50-59 & 60-69 & 70-79 & >79 \\\hline \text { Number of senators: } & 5 & 30 & 36 & 22 & 5 & 2\\\hline\end{array}$$ What is the probability that a senator is under 70 years old given that he or she is at least 50 years old? (A) 0.580 (B) 0.624 (C) 0.643 (D) 0.892 (E) 0.969

All right. So we need to find the probability of a person being aged 18 to 44 years, given that a smoke. Okay, So, off course, the first thing we need to do is compute a product of those common rolls of the last two columns here. So I do point for nine times point 23 That gives us 230.11 to 7. Now that second roll point to 4.34 times 0.22 gives us corn. 07 or eight. Then we have 0.9 times 0.12 gives us 0.1 08 And finally, the last one should give us. It's zero point 00 for eight. Okay, Now, let's add up all these numbers together. Get ah 0.11 to 7 plus 0.7 for eight plus point. 01 Oh, wait. Plus quite Oh, for it. That gives as a total 2.203 What? OK, so social, Asking for age between 18 to 44. We're looking at the first row of this table here. And ah, by based rule, would we just do is multiply The foot is take the first product, which is 0.11 to 7 and divided by the total of all these products. Joe Poi to 031 Okay, so 0.11 to 7. Divided by point. Ah, 2031 That gives us around 0.55 five. Thanks for watching.

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

For this problem, we are given a table which shows the results of a survey of randomly selected us residents ages are in different age categories. For part A we are asked to find the associated relative frequency distribution. So our first step is to determine what end should be Should be 20 plus 21 plus 46 plus 13, which we should note is equal to 100. Which makes sense. Considering we're told that this this row here is a percentage. That also makes it very easy to convert this to a relative frequency. Because we basically just need to convert this from decimal into or from percentage into decimal. So 20 become 0.2, 21 becomes 0.21, 46 become 0.4, six And 13 become 0.13 then for part B. Whereas to find the relative frequency that is a resident is 30 years or older. So problem or relative frequency of Just write it as greater than 30. Well, that's going to be The relative frequency that they're 30-64 Plus, relative frequency that they're greater than 64. So that would be 0.46 Plus 0.13. Which then is going to equal 0.59 as the relative frequency

Even standard normal distribution. We are new zero. We know and sigma is one posted steady or standard normal distribution. We have to find the value of probability between their disposed has 2.1, 1 and 4.0. So this is 2.11, another one is 4.00. And we have to find the inside area. This is the inside area. We can write for lTO ZG better than 2.1 and less than 4.00. There will be The same as for until that less than 4.00-. Girl feels that less than 2.11. This book value from the table comes out to be the last zed less than This value. 0.999 98. And another Valerie two point when one comes out to be zero point 98 645 25 cents. So this is 25 cents. Final answer will be just subtract the value. Yeah. 0.17. This is a valid European. Yes


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