beginarraycchline-score-frequency-hline-90-3-hline-85-2-hline-80-3-hline-75-7-hline-70-6-hline-65--3

Question

$$\begin{array}{|c|c|}\hline Score & {Frequency} \ \hline 90 & {3} \ \hline 85 & {2} \ \hline 80 & {3} \ \hline 75 & {7} \ \hline 70 & {6} \ \hline 65 & {4} \ \hline\end{array}$$
What percent of the scores are within two standard deviations of the mean?

Trinity Steen · Accepted Answer

Okay, So in reference to that questions 24 we were able to get the average was 75.4 and the standard deviation was 7.7. We still know that information. Or to be able to answer 26. That&#x27;s why that&#x27;s there. Um, So the question now is changing from what percentage was once denied aviation out too soon deviations. So we already have one. Senate aviation was a 3.1 and then minus one, Senate aviation was 67.7. So we just had to take away another 7.7 in to get to center, deviations away. And then we&#x27;re going to dio, uh, add 7.7 to get to dinner. Deviations away in the positive direction. So 83.1 class 7.7 is 90.8 and then 67.7 minus 7.7 is 60. So it turns out all of our test scores wherever they were, um, were between 65 90. So all of them all 25 or 100% actually end up being within two standard deviations

Trinity Steen · Answer

vincey table. So we need to figure out, um, how many of these scores or items were going to fall within the once in a deviation. So in order to figure that out, we have to kind of draw ourselves or think of ourselves of a number line right down the middle is going to be our mean the center. And that&#x27;s going to 75.4. And then if I were to go one standard deviation, uh, and one center deviation down, that&#x27;s a matter of adding the 7.7 to adding the 7.7 to that and subtracting a 7.7. So we&#x27;re gonna do 75.4 plus 7.7. That gets me 83 point one. And if we do 75.4, minus 7.7, that gets me 67.7. So if you recall there were 25 of these items and so we&#x27;re just trying to figure out how many out of the 70 hurt out of 25 will be within that once an innovation. So it&#x27;s the range between 67.7 and 83.1, so basically we can&#x27;t count the nineties. We can&#x27;t count the advice. We can count the eighties. So there were three eighties plus the 7 85 that&#x27;s 10 so far and then the six seventies, because we can&#x27;t get so they&#x27;re 16 out of 25 and a set percentage. So you&#x27;ll do 16 divided by 25 move your decimal place. That&#x27;s gonna be 64 percent.

Trinity Steen · Answer

So for this problem and a few others after this problem, you&#x27;re going to be needing to look at that frequency table. So frequency means how many times it occurs. So that means there were three different nineties. There were 2 85 3 eighties and so on. And so if we&#x27;re asked to find the variance Nissinen deviation of these values, we&#x27;re gonna have to still find the mean first. So if there were 3 to 376 and four that those are the numbers we need to add up to make up our denominator. So we&#x27;re gonna add up Three plus two plus three plus seven plus six plus four. That&#x27;s 25. So there were 25 total tests of people or whatever the situation was from the problem. Okay, so now we&#x27;re ready to add up all its members. Now, the easy way to do this is to kind of think of it like this If there&#x27;s 3 19 3 times 90 plus two times 85 plus three times 80 and I can help save you some time. And you calculated from adding up all of those numbers so three times 90 plus two times 85 plus three times 80 plus seven times 75 plus six times 70 plus four times 65 gets us 18 baby five. I am ready to divide that by 25 70. Look, 75.4. Okay, So in order to get the variants, we&#x27;re gonna have to use all of the all three nineties have to be subtracted from the 75.4 and squared. Um, but here&#x27;s thing. If you go and do that calculation for one of these for each of these, then and then square it, you would basically be ableto then multiply by three multiplied by two and so on. So you&#x27;re not necessarily repeating at all these steps in your calculator if you can keep track it like that. So we&#x27;re going to keep going with that same momentum. So Step two is going to be fighting the variance. So what I&#x27;m gonna dio is I&#x27;m gonna do one of each. I&#x27;m gonna dio 90 minus 75.4 and then remember, we&#x27;re still squaring to get when we do our variants. But then when we&#x27;re done with that week in times that by three and use that as part of our final answer in the end or final steps of 90 minus 75.4 and then we square it and we get 213 point 16 So that means there&#x27;s gonna be another to 13 points 16 and yet another two. 13.16 All right, so now the nineties or done Now move on to the 85. So we have a five minus 70 five point for and then square. So 85 minus 75 point or and then squared is 92 0.16. And since there were two of those were going to start another 92.16 down. Now there were three eighties, so we&#x27;re gonna dio 80 minus 75.4 Army Square A T minus 75.4 squared is 21 0.16. And so there were three of those. So another way to think of that is to just times that by three. But Sri kid do that now or later. There&#x27;s not really a huge deal or difference, So I&#x27;m gonna just do that Now we got 63 point for eight. So later on, we&#x27;re gonna have to be adding up all the numbers of Catholic it most at surgery 80.48 later and old kind of have to go for 17 many ways to their seven of those That be a lot of writing that we don&#x27;t stealing you to dio the 75 minus 75.4 squared. So, you know, high by 75.4 is 0.4 square yet 0.16. So since they were setting of those, we&#x27;re gonna times 0.16 times seven and we get 1.1 to So we&#x27;ll use that number later when you need it there. Six seventies. So we&#x27;re gonna dio 70 minus 75.4. I am very square that they&#x27;re 70 minus 70 car point for squared. It&#x27;s us 29 0.16 And because there were six seventies, we&#x27;re gonna have to multiply this by six 1 74 0.96 Last one is 65 therefore of those, So we&#x27;re gonna dio 65 minus 75.4 squared and that&#x27;s 108 books 0.16 times four gets us 4 32 0.64 So recall that variance is all adding it all the times that we just calculated and taking the average of it. So we&#x27;re going to need to do to 13 plus 2 13 plus 2 13 plus. It was to 13.16 to 13.16 plus 2 13.16 plus 2 13.16 plus 92.16 plus 92 0.16 plus. Now we already did this math. So we want the 63.48 getting at it since very did that. So just be careful that you don&#x27;t over over do that. So then 63.48 plus the 1.12 plus the 1 74.96 plus the 4 32.64 So we end up getting our variance is going to be 14 90 six, divided by the number that was in the list. So we determined earlier that the number the list was 25. So divide by 25 when you get 59 0.84 Exactly, actually, so we don&#x27;t need the swiftly equals approximation its attacks equal. And then the square root of 59.84 will get us our standard deviation. So senior aviation is gonna be about seven point seven or 7.74

Abigail Carden · Answer

So here we know that test scores are normally distributed with a mean of 85 a standard deviation of five. And we want to find what percentage lies of scores live between 85 95. So we&#x27;ll start by labeling our bell curve. And so in the centre for me we had 85 then one standard deviation above and below would give us a tea and 90 because we&#x27;re adding our center deviation or subtracting it our second deviations on either side. We have 75 below and 95 above. And for our third standard deviations, we have 70 below and 100 for our above. So we want to find the percentage of scores that lay between 85 95. So because this is normally distributed, we know what percentages of scores like between sander deviations. So we know that 34% is from one standard deviation to the mean 13.5% lays within one state or deviation in our second suitor deviation. So with those values in mind, we can add them up and find what percentage lies from 85 to 95. So our percentage is equal to 34 plus 13.5, which gives us 47.5%

Melissa A · Answer

we&#x27;ll start by drawing a picture for a. The important thing to know about the 80th percentile is that it is the value such but 80% of values are less than it. So in other words, the area to the left of songs that score is equal to 0.8. So in order to find this, we&#x27;re going to use our Sandra normal table and we&#x27;re going to look for the area that corresponds to 0.8. So we started the top. We see that these values are all way too small. So we keep going, Keep going. We scroll down here and we look for 0.8. So the closest values on here 20.8 are these two values right here. So the one on the left here corresponds with us. That score of 0.84 and this one corresponds with us. That&#x27;s where 0.85 So we know where answer is gonna be somewhere between 0.84 and 0.85 So a good guess would be 0.845 And for B the middle 75%. It&#x27;s going to be Sarah 0.75 in the middle and there&#x27;s gonna be two zone scores that bound to this area. We can calculate the area in the tales, so we know that the total area needs to add upto one, which tells us that in either tail we&#x27;re gonna have 12.5% or 0.1 to 5. So we&#x27;re gonna find thes n score on our standard normal table. There corresponds with an area of 0.1 to 5. So we go back to our normal table, you scroll up and we&#x27;re looking for 0.1 to 5. So we find that our answer is going to be somewhere between these two values. These are the closest to 0.125 on this table on this one on the left. Here corresponds with negative 2.24 and the one on the right corresponds with negative 2.25 So this value is somewhere between negative two point 24 and negative 2.25 So a good guess is going to be negative 2.245 for the value on the left and then this value on the right. We know that the normal distribution is symmetric. So this value was simply going to be at the positive version of this number. So is 2.245 on the right. So these are the two sat scores, such that the middle 75% is contained between them.

Zachary Zhao · Answer

Okay, so this question asks around, how much percent of your data, given that it&#x27;s a normal distribution will fall in between to certain intervals on Romo distribution. And this question, the intervals are in between. Our interval is in between Selma right in between one standard deviation below one standard deviation below. And, uh, it&#x27;s your standard deviations above, um So there are two ways to get this answer. First, we refer to this nice little diagram that the book gives us with the traditional percentages of data in, like a perfect normal distribution on beacon. Just look for these, and you could just look for the end points of our interval, which is one standard deviation below which corresponds to negative ones to enter deviations and two standard deviations above, which is right here. And we could just add up this thes percents of data in between negative one and two, and we just do we get 34 plus 34 plus 13.5. So the reformists before 68 plus 13.5 is what? Um, so 0.5 goes over a plus three is 11. So 81.5% of the data Yes. Okay, so that&#x27;s the first way to get it on. The second way is to use your graphing calculator. Um, you have a t I 84 like me. Then this step will be super easy. So the book actually provides more information about this, but basically, we go to the way we go to second, and then we go to bars, variables, um, that the button is variables, and then we go to normal CDF um, and then we take the normal cdf of for the minimum, which is negative one, the maximum, which is two and that are mean under standard deviation are just gonna be zero and one. Um, this way. Um, we&#x27;re allowed to take negative one and two azar minimum and maximum for this case, and we should get around the same answer. Keep in mind, this will be in decimal form, so you might have to most like my 100 to express it in a percent. But either way, you should get 81.5% of data in between these two intervals. So that is your answer

Problem

Jackson $\qquad$ Washington $\qquad$ King 170, 1…

Problem 26 Medium Difficulty

$$\begin{array}{|c|c|}\hline Score & {Frequency} \\ \hline 90 & {3} \\ \hline 85 & {2} \\ \hline 80 & {3} \\ \hline 75 & {7} \\ \hline 70 & {6} \\ \hline 65 & {4} \\ \hline\end{array}$$
What percent of the scores are within two standard deviations of the mean?

Answer

100$\%$

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