use-the-following-information-a-standardized-math-test-has-a-mean-score-of-200-and-a-standard-devi-2

Question

Use the following information. A standardized math test has a mean score of 200 and a standard deviation of $15 .$ Find and interpret the z-scores of the following math test scores.
$$179$$

Zach Steedman · Accepted Answer

okay, We need to find some Z values. And if you look a couple pages back, they say that Z values you, take the data point, subtract the mean from it and then divided by the standard deviation. They tell us right away the meanness 500 standard deviation is 100. And so I&#x27;ve gone ahead and just plug this in to Google Sheets. Example. I&#x27;m gonna walk you through step by step. How I did this on my computer. I took each of one of these subtracted to mean divided by the standard deviation. So let&#x27;s take a look first I said, OK, take this. Selby, too. And I apologize that that too wasn&#x27;t there, but this is two and three and four. But anyway, take this cell and subtract 500 and I just clicked enter, and that&#x27;s exactly what it did. You could do it by hand pretty easily to see that 500 20 minus 500 is 22. Do all these by hand as well. But I just let my calculator do all that work for me. And these are the values I got. Not surprisingly, when we subtract this from 500 Of course, we&#x27;re going negative because these two are the two values that are below 500. So if you do that Mice 500 Yep. We&#x27;ll get negative values and 500 miles. 500 0 next. So just kind of rewinding. What we did is subtracted from the mean Now we got divided by the standard deviation. So to do that, all we had to do notice is take each of these cells and say, Hey, divided by 100 for me. And so is this a cell C two again? There&#x27;s a to here is the three here, take the cell divided by 100. Do that for me five times and I&#x27;ll get my Z values. And there they are. So that&#x27;s 200 divided by 100 150. Divide by 100. And not surprisingly, these values look similar to these values, except if we move some decimal points over two spaces. So there they are,

Wendi Obritz · Answer

and this question were given a sample mean 1 20 on a center deviation of 20 and were given several Z scores and asked to find the data value that corresponds to them. So the formula for the Z score or standardise score is X minus X bar over s. Where is he? Is your standardized score? Exes, Your individual data value expert is the mean of that sample and s is the sample standard deviation. It&#x27;s a part of the question says the Z score is equal to zero. So that happened to do a whole lot of calculation. We could find out that this data value would have to be equivalent to the mean because it&#x27;s neither above nor below its zero standard deviations away from the meat in part B were given a Z score of 1.2. So what data value corresponds to a Z score? That is 1.2 standard deviations above the mean. So we&#x27;ll substitute all of our given information into our formula. Mn simplified someone a multiply both sides by 20 and we find that these will multiply out. So 20 times 1.2 is 24 and then I can add 1 20 to each side and our data value that corresponds to this Z score then would be 1 44 Yes, So this procedure will be repeated for every Z score. So part C, we are given the Z score is equal to negative 1.4. So again, I&#x27;m going to repeat that same procedure, substitute my known information into my Z score formula and solved. So if I multiply both sides by 20 I&#x27;m gonna get negative. 28 is equal to X minus 1 20 And when I add 1 22 both sides, I find out that the data score is 92. So, uh, kind of mentally just confirming the sea score was negative. So I&#x27;m getting my data value is below the mean so that makes sense and a little bit more than one standard deviation will of the meat. So now I&#x27;m on the right track for Part D. We&#x27;re given the Z score of 2.5 So something that&#x27;s a little bit more than two standard deviations above the mean some could expect my answer to be greater than 1 20 by a little bit more than two times 20. So a little bit more than 40 Greater 1 20 So multiplying both sides of the equation by 20 41 equals X minus 1 20 Adding 1 22 both sides. We find out that this data value must be 161. Let me just clean that up. So 161 is 2.5 standard deviations. Better then want one.

Derrick Hanson · Answer

All right, This is a Z score question. So have gone ahead and written out the formula for Z score. The way you find a Z score, Jersey score is equal to your data value minus you mean divided by the standard deviation. I wrote it out What they actually mean. And then I did write the symbols over here. So the blue X just represents, you know, just basic X. Whatever your data value is, X with the line over, it represents the mean That&#x27;s the statistical representation for a mean and then on the denominator. That is a lower case, Sigma. It&#x27;s a Greek letter and lower case Sigma represents the standard deviation in this case. All right, so the problem that we&#x27;re given tells us that we have a Z score of 1.25 tells us our grade, meaning our data value is 60. And it tells us that we have a mean of 50 and then it asks us, What would the standard deviation for that be? So we use that liver case signal just like the book does for standard deviation. Okay, So while this is Aziz core question, now that we&#x27;ve plug stuff into the formula. The rest of this is really just basic algebra of that. We have an equation. We need to solve it out for the variable. Okay, so first thing I would do I see I have a 60 minus 50 up there. I&#x27;m gonna go ahead and combined those. So I&#x27;ve got one. Whoops. Forgot to change colors. So I&#x27;ve got 1.25 equals 60 minus 50 is 10 divided by signal. All right, So if I want to get Sigma by itself, that&#x27;s the goal. First things first. My issues signals in the denominator. I&#x27;m not trying to solve for one over signem trying to solve for signal. So I need to get that signal out of the denominator. Uh, opposite of division. There&#x27;s multiplication as we know. So I would say best option here would be to multiply by Sigma on both sides so that we can get it out of the denominator, will slow in changing colors here, apologised. So that would cancel out the signal here that would leave us with 1.25 times. Sigma is equal to 10. Well, now that I&#x27;ve got 1.25 times the signal. I&#x27;m trying to get by itself. The opposite of multiplication is division. So I simply just need to divide 1.25 to the other side. And I should have my answer. If you take 10 divided by 1.25 you should get that Sigma is equal to eight. So eight is our standard deviation in this scenario.

Tony Wilson · Answer

So we want to find the Z score of the value 18 if the meanest 25 the standard deviation is five. So using the Z score Formula 18 minus 25 divided by five Is this a Z score of negative 1.4?

Bryan Meares · Answer

25 Supposed a normal distribution has a mean of six and a standard deviation of one point buck. What is the Z score of X Equals five points. In order to calculators the score, we&#x27;re gonna take our value of point above, Forgot to subtract. It means we&#x27;re gonna divide by the standard deviation. In this case, we get negative. You&#x27;re a point, Bob, that about one point About which is negative. 0.3 three.

Problem

Use the following information. A standardized mat…

Problem 10 Easy Difficulty

Use the following information. A standardized math test has a mean score of 200 and a standard deviation of $15 .$ Find and interpret the z-scores of the following math test scores.
$$179$$

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