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Delermmne Ihe sample &1z0 needed consnuci ? 95", coniidence itarval #scimate Inu averagu GPA lor tho sludent populalion nual 0.6. Assume the slandan daviat...

Question

Delermmne Ihe sample &1z0 needed consnuci ? 95", coniidence itarval #scimate Inu averagu GPA lor tho sludent populalion nual 0.6. Assume the slandan daviation niine GPA {or ha shudeni Docwlationcollge =MaioiniorThe trmp Eizeneededis (Round (ho noarest Integot )

Delermmne Ihe sample &1z0 needed consnuci ? 95", coniidence itarval #scimate Inu averagu GPA lor tho sludent populalion nual 0.6. Assume the slandan daviation niine GPA {or ha shudeni Docwlation collge = Maioin ior The trmp Eizeneededis (Round (ho noarest Integot )



Answers

Undergraduate GPAs It is desired to estimate the mean GPA of each undergraduate class at a large uni- versity. How large a sample is necessary to estimate the GPA within 0.25 at the $99 \%$ confidence level? The population standard deviation is $1.2 .$

Problem. 14 is dealing with freshman GP eight and the problem gave us 36 individual GPS. That's a sample from the freshman population, a standard deviation of 0.62 And so, with the information given, we have to determine the sample mean the sum of all the GP is given is 101.5, and we need to divide that by the total number of GP is given just 36 that gives us two point A to each GP. A given had just one decimal, and when you're given raw data, your round up your mean by one extra decimal than given and where X to estimate the true mean GP of the freshman class been 99% confidence level. We then need to determine the Z Valley that's associated with a 99% confidence level, and that's 2.58 We will now use the falling to construct our confidence interval, and we just need to plug the values in. So we have 2.2 plus and minus 2.58 multiplied by 0.62 divided by the square root of 36. I would then end up with 2.82 plus and minus zero point 27 and I will use this information to construct my confidence interval. On the left side, I'll have 2.8 to minus is your 0.27 and on the right I'll have 2.82 plus 0.27 My true mean of GP is between 2.55 and 3.9

We're gonna find the GP of the student's grades and rounded to the nearest thousands. So to find GP, I need two things. I need the credit hours and Lenny the total grade points. So to find the credit hours total, I'm going to add this middle column with all the credits. So we take five plus three plus three plus four plus two, and I get 17 total credit hours. Next, we're going to take the credit hours, and the grade combined to figure out the grade points how much it was worth. So to find those great points, you also have to know your GP a scale so a is worth four points. B is 3.5. Sorry, B pluses. 3.5 B is three c plus is 2.5 and then you just follow that pattern. So all the way through, we get that g p a scale. So with that in mind, I'm going to take how many credit hours it waas and then multiply it times however much it was worth like on this 1st 1 it's five credit hours and then a B is three points, so it's only five times three on the 2nd 1 It was three kept credit hours, and it was 3.5 points on the 3rd 1 It's three credit hours, but it's 1.5 points because that D plus on the 4th 1 it's four credit hours and it's two points. And then on the last one, it's to credit hours and four points. So I want to add all these together to get that total grade point. So if I type all these my calculator five times 33 times 3.5 3 Temple in half, four times to two times four and I Adam all up, then I should get 46 great points. So to find the g p A, we take those grade points and we divided by the hours. So we're gonna take 46 divided by 17. 46 divided by 17 rounding it to three decimal places because it's around it to the nearest 1000. I get 2.7058 This eight rounds it up so that my final answer I'm gonna call it 2.706 and that's the G p A. For the student

We want to find the students grade point average based on this report card, and we're going to do two things to find that grade point average. First, we're gonna figure out the number of credits the student has and then figure out the number of total grade points and then take those great points divided by credits to find the average. So to find the number credit that simple, we just need to add together this middle column. So I d five plus three plus three plus four. I should get 15 total credit hours now to find the great points. We're gonna actually put these two columns together over here to make great points. And as we're doing that, we're gonna multiply how many credit hours they were times how much they were worth. So you need to know that great point scale and A is worth four points. A B plus is 3.5 A. B is three. A C plus is 2.5 and then just follow that pattern. So, for instance, on this 1st 1 there were five credit hours, and then it was a B grade, so it's five times three on the next one. There were three credit hours. It was a C plus grade, so it's three times 2.5 on this 3rd 1 It's three hours and it's an F and F zero. If I followed this pattern through and then on the last one, it's four times. See, um, see is a 2.0, if I were to follow this pattern so it's four times to, So I need to go ahead and add those together. So it's 15 at 7.5. It's eight. If I add together 15 7.5 and eat, I should have 30.5. So then, for that last step to find the grade point average, we're gonna take that number of points and divide it by the credit hours to find our g p A. So we're taking this 30.5 and dividing it by 15. When I do that, I get 2.33 and I want to stop with three decimal places because I was asked to round to the nearest 1000 so to three decimal places in my final answer

So we want to find the students grade point average rounded to the nearest 1000 based on this class list this report card we seen So there's a couple things we need to do. First of all, we need to figure out how many total credits there are, and then we're gonna figure out how many total grade points there are. Then I would take those great points and dividing by the number of credits. So to find the credit total, you're just gonna take this middle column and add them all together. We're going to three plus three plus three plus four, so that should be 13 total credit hours. Next, I want to take the grade and the credits and combined those. So we're gonna be combining this way to make the total grade points. So the grade points. So here's what you gonna do for the great points. We want to know how much it's worth. And then how many hours it waas So you're great point scale goes a is a 4.0 A B plus is a 3.5 B is a three and then so on and so forth. C plus would be 2.5 and then just follow that pattern, moving down by the haps. So a B is three points and we had three hours of it. All right, we're going to three times three on that one. For English. A C is only two points, and then there were three credit hours there for history to be plus, so it's 3.5 points for three credit hours, and then the best when we have here is chemistry. It's an A. So it's a four point. Oh, and there were four hours of it. So now we can make each of these into a number total. We're gonna just add all these together to figure out the total number of great points. So each of these making them into a number, answer here. If I total these together, then the number of grade points is 41.5 for this particular student. So now to figure out your G p A, we take the number of grade points 41.5 and divide them by how maney credit hours that were so dividing it by 13. And when I take those together I get 3.192 because I wanted to round it to the 1000 which is the third decimal place


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