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Itemized Charitable Contributions Theaverage charitable contribution itemized per income tax return in acertain state is $792. Suppose that the distribution ofcontr...

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Itemized Charitable Contributions Theaverage charitable contribution itemized per income tax return in acertain state is $792. Suppose that the distribution ofcontributions is normal with a standard deviation of $103. Find thelimits for the middle 78% of contributions.Round z-value calculations and final answersto 2 decimal places.The lower and upper limits for themiddle 78% of contributions are respectively $ and $

Itemized Charitable Contributions The average charitable contribution itemized per income tax return in a certain state is $792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 78% of contributions. Round z-value calculations and final answers to 2 decimal places. The lower and upper limits for the middle 78% of contributions are respectively $ and $



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The average charitable contribution itemized per income tax return in Pennsylvania is $\$ 792 .$ Suppose that the distribution of contributions is normal with a standard deviation of $\$ 103 .$ Find the limits for the middle $50 \%$ of contributions.

Regrets Medium on trees given plan legis average about did you know, lost With a standard deviation of $54. Therefore we have New X is equal to 32. Didn't Sig Mayes? Yes, 50 Fort? No. We have to find the meaning. Standard deviation of the daughter memories. Total amount raised its 1 20 people calling pledges. So we have to find yours. Explain place 62 This to export two days since the pledges or independent off each other. You're right, he does. X 12 legs 1 20 That is your x one plus x two. There's X form 20 that is equal. Do you fix one Lazio X two this to your fates one. Drink tea so your face is given a study toe. So 1 20 times. How do you to that is equal to 3840. Next, we have to find the standard deviation of the total number problem or praised. Who won 20 pledges? It's OK. Begin died of in 120. Bandon really does independent. And then really those explain extra next 20 it is equal to scrape it off Meetings Wolf X one goes extreme two legs. 1 20 That is equality, radiance and fix. One was made until next to this to brilliant. So affects 1 20 You know the raid until fix this 54 square. So that is equal to 1 20 times de foursquare. That is equal to okay. What do you like? 349,000 9 20? That is equality. Fine. I do one point. Quiet. $4. Next. We have to find out what what assumption we made in answering the question. So we assume that the pleasures or independent off each other

In problem 60. We have a normal distribution with a mean of 70 you equal 70 and the standard division of 12, which means Sigma equals 12. We want to determine the limits that includes the middle 65% of the cases. We want to calculate the limits. Four. 65% of the case. Let's recall the normal distribution, the normal distribution like that we have here. The mean it's centered about the mean 70 and has a Norman or a standard division of 12, which means we want now to determine elements that lower limit X one, for example, the upper limit x two. These limits include 65% of of the cases, which means this area showed equal to 0.65 Then what is this area? The allotted area. Here we can calculate the area as it equals the total area. Under the normal distribution, which is one minus the area between the limits, which is 4.65 Divide by two because one minus 4.65 gifts the total area to the left of X one and to the right of X two. But we want to get only the dotted area here which equals one minus, opened 65 by by two. So we divide by two. Then this area equals 4.175 Now we can use the standard normal distribution tables to get. Does it value corresponding to X one? The standard values is one is zero Sorry. Zero. This is a standard value for the mean and we have here that one. And here we have that too. So we can get that one using the normal distribution tables, the standard normal distribution tables by entering and getting the corresponding that value to this area. Let's enter the table. We have here the areas to the left of the school. We will search the tables for 4.175 We have here 2.1 seven four we have here. Oh boy. In seven 4.176 Which means we can choose this value to represent 4.175 because it's the closest one and the corresponding Z score or that value is minus 4.9 01 23 Then that one equals minus 0.9 three. This corresponding to the minus a 0.93 and because of symmetry, the two will be 4.93 We can use the formula by transform transforming from X to set, which says that that one equals x one minus mu divided by sigma or we can get X One equals that one multiplied by sigma and to blow it by sigma Plus you. And of course, we can get X two by multiplying exit to buy Sigma plus me, then X one equals minus 0.93 multiplied Boy Sigma, which is 12 plus 17, which equals 58.84 and X two is all 0.93 complied by 12 plus 70 it equals 81.16 which means the limits, or 58.84 and 81.16 which includes 65% of the cases.

Are We want to find the sample mean extra the sample standard deviation s and construct the 90 confidence interval about the population of meaning you or data below. Reassuming population is normally distributed. And once we compute these particular values, we want to interpret our findings to start off with, let's find, expiring s. Remember that to do so we use appropriate definitions for X bar that is the some of the data X I divided by the end. The number of data points. This computer expert equal 62.3 Ash is defined as the square root of the sum of deviations about the moon square, divided by n minus one. Which in this point computes to 8.0. Next let's find the TC value or rather the critical T value from the student's T distribution needed to compute this confidence interval to do so, we have to use a tea table, A tea table takes as input to important things, the degree of freedom in this case nine and the confidence level in this case .9 to output the correct value, we find we use a tea table either from google or on a textbook and doing so, we find T C. Equals 1.833 next we want to compute the margin of Arafat's interval, given by the formula on the left, plugging in T C. S and end for this problem. We obtain E equals 4.6 and we can compute the confidence interval. Now, given the following formula experiments, E is less than you as less than expert plus E plugging in our experts and our E gives confidence interval 57.7 is less than you is less than 66.9, which we can interpret to mean. We are 90% confident that the new the population mean is between 57.7 and 66.9.

But all right, so for number five, we need to find the variants listening deviation. Before we do that, we have to find the means of all of these numbers in the given list. So this list is pretty large. Turns out there are 17 numbers in this list. So what you're gonna have to do then is add up all those numbers and then divide by 17. So we're gonna do that first. Um, so we're gonna have 43 plus 56 plus 78 plus 81 plus 47 plus 42 plus 34 plus 22 plus 78 close 98 plus 38 plus 46 plus 54 plus 67 plus 58 plus 92 plus 55 altogether gets us 989. So we're gonna write down 989 here and we to divide by 17. He and we're going to get a decimal that we're gonna have two rounds that were in around the nearest town, so you should get 58.2 approximately. Now. This 58.2 this mean is very important because that's how we could measure the spread or the variance from the mean. So we're going to use Bean and bitterly suffuse all of these numbers in this list and subtract this number from the mean with the mean And then we got a square it. Now, the reason why we square everything is because we want to keep things positive so again, Army and is 58.2 and we're going to reuse this number several times in this list of 58 point to 50 point there, 58.2, 58 0.2 stone. Yeah. I mean, is very important to get to use quite often in these problems. Hey, Stared. This is one of the longer ones because the list is so long not gonna have this long of a list. And if you have access to doing something with technology, like to be able to find this with technology and get your allows that that's 100% okay. But that's just how you show your work if you are required to. All right, so we're gonna subtract and square, so really go ahead and go through the list and do that. So 43 on a 58.2 gets me a negative. But remember, when you square negative, you get a positive. So you should get to 31 0.4 for that 1st 1 56 minus 58.2 squared gets us 4.84 You're OK. 78 minus 58.2 Squared 3 92.4 81 minus 58.2 Squared 5 19.84 47 minus 58.2 squared. Get this 1 25.44 40 to minus 58.2. Squared gets us to 62.44 and then ready for the next column. 34 minus 58.2. Squared gets us 5 85.64 20 to minus of the 8.2 on. Dsquared gets US 13. 10.44. It's a bigger number. All right, 78 minus 58.2. Gives us 19.8 squared. It's US 3 92.4 Okay, 98 minus 58.2 squared. It's this 15 84. That's a 12 0.4 All right. 38 minutes 58.2 squared. Get this. 408.4 46 minus 58.2. Gets a snake it of 12.2, but were squaring that we get a positive 1 48 0.84. Then 54 minus 58.2. Squared gets a 17.64 on this last call. Okay, 67 minus 58.2 is 8.8 and we square that 77.44 look a little nicer. 0.44 All right, 58 minus 58.2 squared. Get this point. 04 90 to minus 68.2 and then squared. Get this. 11. 42 point 11. 42 point for four. Your point for now. Okay. And then 55 minus 58.2 squared gets us 10.24 So after all that tedious work, I know that was a lot because our list was so big. Um, we're going to need to actually get the variation. So we get the variation by taking all three numbers in these columns, and we'll add them all up and find the average of that that was just the various. So it will take a little bit, but it will be fine. So we got to 31.4 plus four 0.84 plus 3 92.4 plus 5 19.84 plus 1 to 5.44 plus 262.44 plus 5 85.64 plus 13 10.44 plus 3 92.4 1584.4 plus 4 8.4 plus 1 48.84 plus 17.64 plus 77.44 plus 0.0 for plus 11. 42.44 This was before for and then last, but at least 10 0.24 We add all those up and we get a grand total of 7000 212.44 We divide by 17 and that will definitely to be rounded. It's 424.3. We take that 424.3 and we need to now use that to get the standard deviation so the sooner deviation is always a square root of the variants that we just got. So we're gonna square root the 4 24.3 and I think that look a little bit nicer. And then we get approximately 20.6 rounded to the nearest tense of make sure circle or square, your Final Two answers air the variance and the senior deviation as 20.6 for number five.


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