make-the-given-changes-in-the-indicated-examples-of-this-section-and-then-solve-the-indicated-pro-52

Question

Make the given changes in the indicated examples of this section and then solve the indicated problem.
  In Example $3,$ find and interpret the $z$ -score of an achievement test score of 630

Barsha Rana · Accepted Answer

Welcome to New Marine in the current problem. It is given that the variable follows a normal 500. That is mean mu is 500 sigma is 50. Okay. And we are asked little brit the significance of the the school of the value. That is a particular value of X. We Excellent but what is it what&#x27;s going on in the school? First student can go back. So it could be uh minus mu by sigma. That is 6 30 minus 500 by 50. That is 130 divided by 50. So this cancels. And we get if we multiply by two inside we get 26 by 10 that is 2.6. So we have to interpret 2.6. Now if we think of our normal distribution standard normal we know it is centered at Mhm. Now next value comes at one sigma distribution differences one two sigma differences to three sigma difference history. The same way over here minus one over here minus two over here minus three. Nothing of the importance this area. This is 65 oh 68 one thing. Okay, entire vista. Mhm. And if we think off this, yeah, this contains 95% of America right? And if you consider the last one, that is the entire thing of it, this contents 99%. So you can understand if I am considering to and then 2.6 would be somewhere nearby too. See? So if I consider this is a pretty rare value because 68% of data would lie between this and ah 95% data would lie between this. So if I think of 2.6 here and here, even that will include a lot of later. That means what the data is more concentrated here. But if you think data, the probability of line between 1 to 2 that is a narrow line. So if you think 2.6 beyond going to 0.6 is pretty less. So probability of the set value would exceed 2.6 is very small. We can find the exact value from the table, but that will be something 010 something. So that value indicates that this is a pretty rare value. Too awkward and that&#x27;s where it is so far away from the center. If it was a regular value, it would have looked like 0.15 inches nearby. This or 1.2 something like this. So this value over here is very rare to walker and so holds true for 6 36 30 is we&#x27;re too occurred. So that&#x27;s the interpretation that we obtain through the standard value.

Thomas Emment · Answer

Okay, we begin. Some said indentations here, and we want Teoh. See them on a bell, curve on, find out their area. So this is my bell curve here. That topic should be on the line. By the way, these bits don&#x27;t go up beside the no point nor eight. Well, that&#x27;s just gonna be from the right hand tail. No point nor a is. You said that she said school here on the air associated with it is well, simply going to be no point nor a when we got the area between North 0.98 nor point. Not too well, no, but not too is this behavior is actually a little further in the North 0.0.8. Change on on this side, you have nor 0.98 and you want although area between this. So the whole thing number nine, it will be the whole thing. And then base it is taking away this area. Here is no point, no to. So what you gonna be left with here is an area off nor 90.0.96 Okay, here, You see, we just do the calculation in the middle and you&#x27;re gonna be left with no point at 99 So it&#x27;s just gonna be the best. The area associate with that. At no point 99 which is an area off no 0.99 under the curve, says communication nor 0.99 on this one, where you&#x27;re gonna have when you minus sing A, um is that value we actually left with mine instead of no 0.975 is actually minus said off one minus. That&#x27;s about North Point, North to five. You actually have a set of noble 45 months of no 450.45. So this is going to be zero.

Bryan Luo · Answer

okay, Is this question asked us to compute Z scores. So the formula for disease score is dressed the value honest, the average divided by the standard deviation. So right off the bat, we know that the average just by taking us I&#x27;m divided by five is 15. And then what you can do is actually use a standard deviation functionary calculator, too. Find the Senate deviation would also do it by hand, but usually, uh, when it comes to business statistics or just advanced to take six classes in general, we like to do it with their calculator because it&#x27;s not really practical to do it by hand every time. So, uh, put it into a calculator and you&#x27;ll see this in deviation is about 3.58 So now to talk with the score always to do is plug in each value to this function. So let&#x27;s talk in the first value 10 minus 15 about it by 3.58 That equals native 1.25 Let&#x27;s talk in a second value 20 minus 15 over 3.58 and that equals positive 1 25 It&#x27;s like in the third value. Um, 12 minutes. 15 over 358 in that equals negative. 0.75 Gonna make a new page real quick. So plug in the fourth value 17 minus her average. Which waas 15 butted by the standard deviation, which was 3.58 And that will give us your 0.5. Oops. Sorry. And finally look at her last value, which is 16 divided by 3.58 which will give us 0.25

Caelan Thomas · Answer

First we want to calculate Z at three negative one, which is going to give us three squared minus three times negative one plus three times negative one squared, which equals 15. And then we&#x27;ll calculate. See at 2.96 negative 0.95 And that&#x27;s going to give us 14.2811 And now if we take Delta Z as the difference between Z at 2.96 negative 0.95 and see a three negative one we get Delta Z is equal to negative 0.71 89 And if we find dizzy Differential, see by taking a partial derivative with respect to X, which is two x minus y TX and the partial derivative with respect to why negative sick negative X plus six y times D y and we have that D X is equal to 2.96 minus three or negative 0.4 And D Y is equal to negative 0.95 minus negative one. Which gives us positive zero point Sarah five. And so we have TZ equals two times three minus negative one all times native 0.4 plus negative three plus six times negative one all times 0.5 which gives us TZ is equal to negative 0.73 which is a pretty good approximation for the actual Delta Z, which was negative zero point 7189

Robin Corrigan · Answer

for this problem were asked to find standard scores said such that the area above the said score but below the mean under the normal curve is equal to such and such and were given these areas in parts A, B and C. So to visualize what we&#x27;re searching for, we&#x27;re looking for his head score such that the area above it but below the mean his equal to x and were given X from the problem so we can use standard normal tables to find X two foot. Sorry to find Zedd. Ah, but note that in a standard normal table, zed scores correspond to cumulative areas to the left of the set score shaded in red. So one thing we can say is that the area covered by the red and the blue is exactly 0.5 because it constitutes exactly half of a symmetrical distribution. So therefore the area in shaded red is 0.5 minus x. So for our problem, we can solve for his that scores that correspond to cumulative areas of 0.5 minus X, where X is the area given to us in the problem feel for part A were given an area of 0.3212 So remember, that&#x27;s the area above the said score and below the mean. So applying our strategy, we can subtract that from 0.5, and that gives the corresponding area of 0.1788 For now, we can look up the set score that corresponds to a cumulative area of 0.1788 So that&#x27;s this area here in the cell. So the score is minus 0.92 and in part B, the area given to US zero point for 788 Using our strategy, we subtract that from 0.5 and that comes out to 0.212 So what is there is that score? So it is a boat somewhere close to here, looking for a 0.212 and that&#x27;s 0.217 So that&#x27;s the closest we can get. That&#x27;ll be good enough. So it&#x27;s about minus 2.2 No, actually, we could get closer than that. We get 0.21 to in that cell. Exactly. So it&#x27;s minus 2.3 and then Part C were given an area 0.2700 So that gives us a cumulative area that 0.5 minus 0.2700 It is equal to zero point 2300 so that&#x27;s similar quite close to this, which means there is. That score is minus 7.0 for its minus 0.74 That gives us as its course minus 0.74

Robin Corrigan · Answer

when this problem were asked to find Zedd scores that correspond to an area above the mean and belittle the said score of the normal curve that corresponds to such and such an area and were given a different area for parts A DNC. So to visualize what we&#x27;re looking for is, let&#x27;s say this is a standard normal distribution we&#x27;re looking for. Some said score such that the area be lewit, but above the mean is equal to a specific value. Well, it just call that X. So we&#x27;re given X in the problem, and we&#x27;re ask yourself, Is that so? Since if we&#x27;re going to use a standard normal table since those tables give us the cumulative area below, said another way to look at this is to consider the cumulative area below said so is equal to this red shaded area, So that&#x27;s going to be equal to an area of X plus 1/2 because it includes. In addition to the area, exit includes the left half of the distribution, so the area shaded red is equal to X plus 0.5 so we can take the values, the areas that are given to us in the parts of the problem, add 0.5 to them and then use the standard normal table to sell for said so. For part, they were supposed to find such a zed score that corresponds to an area of 0.3 962 below this escort, but above the mean, in other words, below the said score, but above zero. So if we convert that according to our strategy, by adding half to it, we get 0.8 962 And so we can look for his ed score that corresponds to a cumulative area of 0.8962 to find our answer. So an area of about 0.8962 is right here, and that corresponds to one point 26 So that&#x27;s your answer. That&#x27;s the said score in Part B were given an area of 0.4846 Once again, if we had have to that get zero point 9846 and to find her said score, we can look it up on the table 0.9846 and that is right here. So that gives us 2.16 so that is equal to two point 16 and then for part C, we&#x27;re given an area of 0.37 12 adding half to that. We can get a 0.8 712 so we want to find a set score that corresponds to a cumulative area. Have zero point at 8712 0.87 12 is just as its course slightly bigger than that, but close enough. So we have 1.13 for there. For hours, that score is 1.13

Problem

Make the given changes in the indicated examples …

Problem 3 Easy Difficulty

Make the given changes in the indicated examples of this section and then solve the indicated problem.
In Example $3,$ find and interpret the $z$ -score of an achievement test score of 630

Answer

$z=2.6$

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Intro Stats / AP Statistics Educators

Catherine R.

Monique R.

Heather Z.

Joseph L.

Intro Stats / AP Statistics Courses

Data And Variables

Data And Variables - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 22

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Monique R.

Heather Z.

Joseph L.

Data And Variables

Data And Variables - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$z=2.6$

Basic Technical Mathematics with Calculus

Catherine R.

Monique R.

Heather Z.

Joseph L.

Data And Variables

Data And Variables - Example 1

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Monique R.

Heather Z.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus