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Arandom sample of SAT exam scores has sample mean of f = 050 and sample standard deviation of f = 150. Use the Empirical Rule t0 estimate the percentage scores that...

Question

Arandom sample of SAT exam scores has sample mean of f = 050 and sample standard deviation of f = 150. Use the Empirical Rule t0 estimate the percentage scores that are more than [ , 350.Round your answer t0 the nearest hundredthProvide your answer below:M Feedback

Arandom sample of SAT exam scores has sample mean of f = 050 and sample standard deviation of f = 150. Use the Empirical Rule t0 estimate the percentage scores that are more than [ , 350. Round your answer t0 the nearest hundredth Provide your answer below: M Feedback



Answers

Determine the F-test statistic based on the given summary statistics. /Hint: $\bar{x}=\frac{\Sigma n_{i} \bar{x}_{i}}{\Sigma n_{i}} .1$ $$\begin{array}{cccc} \text { Population } & \begin{array}{c} \text { Sample } \\ \text { Size } \end{array} & \begin{array}{c} \text { Sample } \\ \text { Mean } \end{array} & \begin{array}{c} \text { Sample } \\ \text { Variance } \end{array} \\ \hline 1 & 15 & 105 & 34 \\ \hline 2 & 15 & 110 & 40 \\ \hline 3 & 15 & 108 & 30 \\ \hline 4 & 15 & 90 & 38 \end{array}$$

Okay, so we're given that population has a mean you off 1 50 Standard deviation 25 on a sample size of 400. Gay. Since this, it's sample size is greater than 30. You can use the central limit serum to conclude that the distribution of sample means is approximately normal with the mean and standard deviation. Quote to mute. Thanks, Andi. Standard deviation inspire which is equal to signal over Groot on don't physical 21 50 onda 25 over the square. Root off 100 which is equal to 2.5, Uh

Yeah. All right, guys, over this problem, we're gonna go ahead and try to find the mean and standard deviation already took the liberty, uh putting in the mid points and the frequencies in there. And so let's go ahead and start trying to find the weights now. Um So the midpoint, of course, um are just going to be the number right smack dab in the middle of each of the ranges, and the frequencies are just copied right from the table, the weights we're gonna find by just multiplying the mid points and the frequencies. So there we go there. Um And so that's gonna be our wages that are mid points under frequencies. And so um yeah, let's keep on going with that. It should eventually start picking up a pattern for us. Doesn't look like it is, but that's okay. Um Okay, and so what we're gonna do there is we're going to take that and scroll down and there we go. Okay, cool. So what eventually picked up a nice pattern for us. It's really nice. Okay. And so of course once a pics of a pattern um we'll be able just click and drag down. All right. And then um Okay. And so what we're going to do next is this we're gonna find the weighted mean. Finding the way to mean is very simple to do. Um You first you just start by hit an equal sign that tells the google sheet. You're gonna do formula. You're then gonna do the some of the weights. Oops, I forgot that part. We have just add the weights first. Let's add the weights in order to add the way to do. Equal some open parentheses and select everything you want. Close and there you go. And then the frequency is also very simple. Just equals um and select everything you want, click and drag. There you go. And so our killer's right there, so are weighted mean, it's simply the sum of our weights divided by our frequencies and there we go. And there is our weighted mean, right there are weighted mean it's just a touch over 600 so that takes care of the first part of part A um And that's what we're also going to do in order to help us for to find the standard deviations were can actually copy that way too mean down a bunch of times. There you go. So we're gonna copy that way to me down a bunch of times and then we're gonna go ahead and find differences. And so the differences will help us find a variation, which in turn helps us find standard deviation. So our first difference is just gonna be our midpoint minus the weighted mean, There we go, and then we'll keep on going. It's going to be the midpoint minus weighted mean there we go. It's probably picked up on the pattern already, usually after two, it picks up on the pattern and there we go. Um So yeah, and of course, if you want to go through and double check to make sure they're right, you can but already did there. Okay. All right, And then um so the next thing we need to do is this we need to go ahead and find the squares of the differences and multiplied by the frequencies. He's not gonna do that, start with an equal sign and we'll do the difference times, or asterisks itself itself, which makes it a square. And then we're going to multiply by the frequency. Perfect, Okay, cool. Next we're going to do the difference times the difference times the frequency you're gonna keep going, it's going to be different part of three manually just to make sure the computer gets it times the frequency. Yeah, here we go. And then it should work from there. Perfect. Okay. That should have worked. If you're scared it didn't work. Here's what you can do is go to one of the bottom of randomly. That's 7695482. Let's see if we can try to make sure it's also same thing. Yeah, it's the same thing. Perfect. You go. So that all happened correctly already. So the next thing we're going to do is this in order to find the variants, we need to add all those guys together so equal some of all of these guys at all those together. And the variant equal to this divided by degrees of freedom, degrees of freedom is simply one less than frequency. Since the total frequencies. So the total frequencies is 5796 degrees. Freedom is going to be 5795 and there is our variance. Okay, now we find the variance, it's going to be very easy to find a standard deviation. We just have to take the square root of the variance in google sheets equal. That's going to be equals S. Q R. T. Open parentheses. Quick on the number you want. And there is our standard deviation. So that takes care of part A quite nicely. All right time for part B. We have to do a frequency instagram. And so we and the frequency instagram is going to be of the mid points and the frequency. So I'm going to highlight all the midpoint of the frequencies and I'm going to go to insert chart and it's not quite what I wanted. Actually, we're going to try again here. No. See uh Okay. It's not quite behaving the way I wanted it to. That's okay. Uh huh. I don't want that. I don't want that either. Let's try that. No, it's gonna work. I promise About that one also. No. uh Yeah. Oh, I don't want to combat shirt uh wine area. Okay. It's not really picking up on what I want. Mm. Everything. Oh, what? Yeah, yeah. Okay. Yeah. Like what happened? Okay. Yeah. Yeah. Uh Okay. I think this is what it's confused about. It should be the X axis. Should be uh huh. Shouldn't be not confused here. No. Yeah. Yeah, there we go. Okay. X axis. The midpoint. Perfect. Okay. I think I got it there. Right. Okay. Perfect. Yes. There we go. Alrighty. So yes, when we do this here. Yes, that's what we want. Okay. So yeah, that is bell shaped a little bit, yeah, unfortunately, sometimes you do kinda have to play with the graph a little bit in order to make it do what you want to do in google sheets. So yeah, and so that's going to be that definitely is a fairly bell shaped, so yeah, that's going to be a bell shaped curve there and so that works out nicely, so that takes care of part B. Okay, cool. So the next thing we need to do is we need to confirm um Conflict 95% of the score, what the 95% of the score? A range in which should encapsulate 95% of the scores. So, according to empirical rule, you want a data .2 standard deviations below the mean. And you want us data .2 standard deviations above the mean. Okay. And how do I find that? And so this should take care of 95 of the data. Yeah. That should take care of 90% of the data. That's 2%ages below and two standard deviations above. Two standard deviations below. How do you find that very simple? You're going to take the mean and subtract two times the standard deviation and there you go into sanitation bob. You're gonna take the mean and Add two of the okay, Intermediation above. There you go. All right. And so between those two data points, that should encapsulate about 95% of your data.

Okay, so we know that the population has a mean she called to 1 15. I standard deviation signal equal to 25 in sample size of 50. So sample sizes good than 30. So we can use the central limit term to conclude that the distribution of sample means is approximately normal with the mean on the standard deviation. Both muse X. I mean, I see myself x physical, too show. And yeah. So this is therefore equal to 1 50. This is equal to 25. 50. Because you have put flesh. Sure. So we're screwed. Oh, contract should be Tom. Yeah. 2.5 36

Okay, So in this question, were given that the population hasn't mean view equal to 1 50 huh? Standard deviation Sigma Michael, the 25 on a sample size and you go to 1000 e sample size, good and 30. Therefore, we can conclude that really used CIA Central Limit serum to conclude that the distribution of sample means is approximately normal with the mean and standard deviation station equal to signal over and on. X is equal to music, which is equal to 1 50 which is equal to 25 for Scrooge of 1000 which gives us an answer of serpents 79 or standard deviation.


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