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Use the table to find the standard score and percentile of the following data values A data value 0.6 standard deviation below the mean: b; A data value 4 standard ...

Question

Use the table to find the standard score and percentile of the following data values A data value 0.6 standard deviation below the mean: b; A data value 4 standard deviations below the mean_ C. A data value 2.2 standard deviations above the mean.Click the icon to view the standard scores and percentiles for a normal distribution_The standard score is and the percentile is (Type integers or decimals-)b. The standard score is and the percentile is (Type integers or decimalsThe standard score is an

Use the table to find the standard score and percentile of the following data values A data value 0.6 standard deviation below the mean: b; A data value 4 standard deviations below the mean_ C. A data value 2.2 standard deviations above the mean. Click the icon to view the standard scores and percentiles for a normal distribution_ The standard score is and the percentile is (Type integers or decimals-) b. The standard score is and the percentile is (Type integers or decimals The standard score is and the percentile is (Type integers or decimals:)



Answers

Find the following percentiles for a standard normal distribution. a) 30 th percentile b) 50 th percentile c) 95 th percentile

Here. In this problem we have to find the main division about the median for the following data. First of all, we will find the median. So in order to find the median, we will arrange the given data in ascending order. We have 10 comma 11, comma 11 comment wells go amantadine, coma 14 comma 16 comma 16 comma 17, Coma 17, Coma 18. Here we have n. s. equals to 12, Which is even so median is the average of 16 7 observation. Therefore we get meeting And which is equals two, 13 Lus 14.2. It would be equal to 13.5. Now, we will find the absolute value of the deviation from the mean that is X I minus median. Uh huh. Here we have meeting is 13.5 so X one minus median would be 10 minus 13.5 since we are finding the absolute value of the derivative. So we will drop the minus sign here, navigate Then -13.5 is 3.5 plus 11 -13.5 years, 2.5 Plus 11 -13.5 years, 2.5 Yes, 12 -13.5 is 1.5 plus 13 -13.5. Plus. 13 -13.5. Plus. 14 -13.5. Yes. 16 -13.5 years, 2.5 Yes. 16 -13.5 is 2.5 Plus 17 -13 17 -13.5. 3.5 Plus 17 -13.5 is 3.5 bless 18 -13.5 is 4.5 It would be equals to 28. Now we know that main division about meeting is equal to van a poner en sigma, Where I goes from 1 to N derivative from the mean main aviation about median is equal to one a 10.12 into 28. It would be equals two, 2.33. Therefore, we get the main division. About million Is equals to 2.33.

So we're looking at the data and we can see that the data goes from 27 all the way up to 34. And if we look at the history, Graham Instagram, uh, looks to be, you know, pretty bell shape. So we would think that this is approximately a normal distribution. Then part B were to look at the normal Quanta will plot and remember, for a normal quantum plot, you're probably not ever asked to make one long hand. I never had my students do that. But you are looking at those values and you're hoping that you're seeing some linearity and so approximately linear. Therefore, the tendency is for the distribution to be approximately normal, not perfect, but not too bad. Then we want to look at on part, see what the inter quartile ranges and, uh, we need We have 50 numbers, so if you have them all listed down, um, if you put them all on your calculator, your calculator will give it all to you with 11 should put one variable stat. But if you have 50 numbers and then you need to count to find the 25th number 26 number, and that number will be your median and that number ends up coming out to be 30. And then we have 25 numbers who are below and so 25 numbers below. If I take 25 divide it by two, I get 12.5. So there are 12 numbers here, 12 numbers there. We need the 13th number in the list counting this way, and we also will need the 13th number counting this way, this one will be our Q one and Q one comes out to be 29 and therefore Q three counting comes out to be 31. And so our inner core tell range is the difference between Q three and Q one is two. And so, in order to find where those whether we have outliers or not, we want to take the Q one, and we want to subtract away 1.5 boxes. So 29 minus three anything below 26 is going to end up being an outlier, and there are none. No low outliers, and then we need to take Q three and add on 1.5 boxes, box wits or recurs. So 31 plus three is 34 anything higher than 34 is going to be an outlier. And our highest number is 34. So there are none. There are no outliers. Yeah, we don't count those that are right at that limit. And then we need to find the Pearson uh, index. And there are two methods for finding that one is the ski Eunice, where we take the mean and subtract away the mode and then divided by the standard deviation. And I have that the, uh I mean, when I calculated was this my mode most frequently occurring number was 30 and then dividing it by the standard deviation which I had had that day to put in my calculator. And I get this as the scariness. So it is positive it's pretty close to zero. So if it's skewed, it's just a little bit skewed to the right. And if we use the second index formula, that's three times we take the mean minus the median divided by the standard deviation. And in that case, it ends up that the median and the mode are the same. So I just finished writing here. So basically three times that quantity that we had up here and this Kunis number would be 30.265 So again, if there is Kunitz, it's skewed just a little bit to the right. And so it appears that this distribution is pretty close to being a normal distribution. Not too bad. You can tell that really from the 22 earlier plots that there's not too much skin this.

When tackling this problem, hopefully have some software at hand whether it's ah, graphing calculator or software online. But really, all you need to do is input these data values into your software. It will calculate the main and standard deviation for you. So in this case, I found a standard deviation calculator online, and I'm going to go ahead and input all of these pieces of data in 89 may push calculating and will give me all the information I need. So the standard deviation between just called SD or you can call it, um, the Scripps Simple Omega. It's 5.6 and then you look around, you see this symbol here, This is mu or in math, that means Mean mu is kind of a fun simple to try to rate of 7.7 and you are all done

So in the next. For gentle represents the day to value that has percent off on later models and for 91% off all data. So we have the person tell below 91 person tell. So we have the area and you've been at the singles 90. 1 person presented us in their symbols. We have sort of a point 91 00 in the disease score table on the statistical table, off normal distribution or off CDF or settled. That's the function. And we have seen that our which is committed dancing t function. We have the girl in the table that three point have a stable from your do that area off 0.910 is sneer at 1.3 us this stance multi frequency that this sickles toe little point 9099 So here the score off 91% it's about 1.30. Yeah, um, the nexus letter B that is given the physicals the percentile 9% on the table. Mhm 0.3, the body off the 3rd 0.97 Children, 9%. It's about up Magothy or or not, for it's a virtually represented as the symbol. We can see the committed distribution of frequency that iss um negative 1.13. It is equals to 0.9 on it is near poor on 9%. So that this core is this oneness equals two negative 1.30 Then you have ah, even that iss better see that it's 75 person person tell so represented on the symbol. So you have you're fine 75 okay. And the normal distribution standard or no standard normal city we have at at 20 0. 70 Bye. Then we can see that we can see if that it's about from should appoint 68 and between 7.68 3 point seven. So we have so that it's between in between death. So we have thescore off this girl's toe 3.67 i the other one is about 25 percentile. We express it as this month. So we have three point 25 the table 8.3 the standard normal car areas. We have the balance Your 0.25 when this is with doing negative six point Oh are negative 0.67 and negative 0.68 So on that between, So so we have data Disciples toe negative zero point 675 the other one the sixth percentile. She will have 6% tal. So 6% presented several points. So we observe Point Shiro six no inevitable 4.8 value of 0.6 It's about 7.6 Should appoint toe negative 2.51? No, that's that. It's about about, say that it's singles toe Tom for negative 1.55 but it's about 3.0 606 Mhm, the off negative. 1.60. But this one store 7.5 94 we have 56 Sean ish 56 should appoint that name before or we have set a pawnshop point for in the between This one's so we have between a d. So we have say that singles toe negative bomb point. Bye Bye Bye. So here we have the goes to 1.30 This one It's neck negative. 30 negative 1.30. This one is about he calls the syrup on 6675 Then this one is about negative 0.675 And this one is this He also negative 1.555


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