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Lecoies i0l petSOMS Wio scoie (#) ,40, (D) MiO, ana (2) 260. Give the TW scores for persons whose Z scores 0n this test are (d) 24_ (2)15. () 0 :d 9) 45 15, Aprson ...

Question

Lecoies i0l petSOMS Wio scoie (#) ,40, (D) MiO, ana (2) 260. Give the TW scores for persons whose Z scores 0n this test are (d) 24_ (2)15. () 0 :d 9) 45 15, Aprson scon"s 8/ 0n a test Of verbal ability and 6.4 0n a test ot quantitative ability: For the verbal ability test, the mean for people in general is 50 and the standard de- viation is 20. For (he quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person` stronger ability: verb

Lecoies i0l petSOMS Wio scoie (#) ,40, (D) MiO, ana (2) 260. Give the TW scores for persons whose Z scores 0n this test are (d) 24_ (2)15. () 0 :d 9) 45 15, Aprson scon"s 8/ 0n a test Of verbal ability and 6.4 0n a test ot quantitative ability: For the verbal ability test, the mean for people in general is 50 and the standard de- viation is 20. For (he quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person` stronger ability: verbal or quanti tative? Explain your answer t0 a person who has never had a course in stalistics: kin



Answers

ITBS scores The Normal distribution with mean $\mu=6.8$ and standard deviation $\sigma=1.6$ is a good description of the lowa Test of Basic Skills (ITBS) vocabulary scores of seventh-grade students in Gary, Indiana. Call the score of a randomly chosen student $X$ for short. Find $P(X \geq 9)$ and interpret the result. Follow the four-step process.

The problem, we're going to be discussing Z scores and how to divide the bounce of um Z scores and the date set with the data set. So we're given that um for I. Q. Scores that the mean is 100 With a standard deviation of 15. So I've driven I drew a sort of normal distribution which is associated mean and standard deviation. It's asking if unusual I. Q. Scores are plus or to our two standard deviations away from the mean, what is the score? So for part a you know that you know if the if the if if um if it's too strange deviations away from the mean disease square must also be too right. So it's negative two and positive too because you can have um a sort of minimum I. Q. That's unusual and a maximum like you that's unusual and to find the associated um the final associated like you for each of the z scores you can just sort of visualize it, right? So the for the for the minimum bounds um you are two standard deviations below the mean, so you do 100 which is the mean of the data set -2 times the standard deviation Right? And this gives us a lower limit of 70. You repeat the same algorithm for the positive to to determine what the upper limit of an unusual of the usual I. Q. Score is. So you do 100 100 Plus two times 15 Which gives you 1:30. So this tells us if your I. Q. Is below 70 or above 1 30 then you have an unusual like you.

So we have information about the 2005 math s A. T. So it is called Meth S a T. And then I'll subscript at math and we're told that it has a mean of 520 a standard deviation of 115 and that it is basically a normal distribution. It's not exactly normal, but it's very close to one. And in part, A. We want to know what is the Z score. If somebody scores a 7 20 what is their Z score? Well, there is these scores what they got, minus the mean divided by 1 15. And so we see that that difference is 200. So let's take 200 divided by 115. And we find out that that is 1.7 roughly four. And that means that the person scored 1.74 standard deviations above the mean mhm. On the other hand, let's go the other way that we know that someone has a A Z score of 1.5 or the person scored 1.5 standard deviations above the mean and with them we want to know what was the person score. So remember the Z score is how many standard deviations above or below the mean So we don't know this score. But we know that this is true. And so with this will be multiplying 1.5 this value times 115 and then adding to that by 220 and we find out that the score would be 692.5. Now you can't get a 0.5 on the test, so it's either going to be a 6 92 or a 6 93. And Park Si is doing a comparison and they're dealing with the 2012 exam. And we know that the, uh, the S A T, assuming that it was math again, had a mean for that year of 514 and the standard deviation of 117 very similar to the previous when we looked at and the A C t, on the other hand, as a much lower point total. But the mean that year was 21 with a standard deviation of 5.3, and we have one person who scored on the S a t so we'll do that in blue on the S A T scored a score of 700 and on the other hand, the person on the scored a score of 30 and we want to know, relatively speaking, did which one did better? So let's find out. So let's go through and figure out what this s a T Z value is how many standard deviations above the mean so 700 minus 5 14. Divided by 117. And let me get that left front to see 700 minus 5 14. Divided by 1 17, the C score is 1.59 So this person scored 1.59 Standard deviations above the me. Now let's look at what happens here. What's the Z score here? And we have 30 minus 21 divided by 5.3. And once again, I'll go left front to see 21 books. I'm sorry. 30 right. Minus 21 which I already knew it was nine. I don't know why I don't just put nine divided by 5.3 and I can't do that. 5.3 division in my head and I get this. See, value is 1.698 So this is approximately 1.70 Standard deviations higher. So this person, relatively speaking, did a better job compared to others. Because this person has a score that is 1.7 standard deviations higher than me. And this one is only about 1.6 higher than the main. So this one is the winner.

This problem. Um This is the tallest U. N. And women's problem. You're given that you know, a man named Sultan has a height of 247 centimetres. And a um women named Day Day Fanelle is 236 7 years old, relative are relative to their appropriate populations. Which one is taller? Right? So relative to their age group, gender groups which one's taller. So to do this you have to find the relative difference between the two. Right? And so you have to find Z scores. The score is a way of comparing what a um Abnormal activity abnormal dataset is relative to the mean of the subset of population. So you simply do 247 which is the height of the tallest man minus the um mean of all men. Right? And so this gives you the delta between what the difference between the tallest man is and the average man is. Right? And so once you have the delta, you then divide by the standard deviation which sends the centimeters and you get 10.3 um standard deviations right? So the man Sultan is 10.3. Standard deviations above the mean. We repeat the same procedure with David. Yau and we obtain A Z. score of 12.3. So you can clearly tell that day fat yell, given that she's a women. She her height is actually 12.3. Standard deviations above the mean of all heights of women. Right? And so therefore the answer for this problem is that data is the taller one relative towards their gender groups.

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's the statistical representation for a mean and then on the denominator. That is a lower case, Sigma. It's a Greek letter and lower case Sigma represents the standard deviation in this case. All right, so the problem that we'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'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'm gonna go ahead and combined those. So I've got one. Whoops. Forgot to change colors. So I'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's the goal. First things first. My issues signals in the denominator. I'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'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've got 1.25 times the signal. I'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.


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