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12_ A sample has a mean M = 50. In the sample, a score of X = 41 corresponds to z = -1.50. What is the standard deviation for the sample?...

Question

12_ A sample has a mean M = 50. In the sample, a score of X = 41 corresponds to z = -1.50. What is the standard deviation for the sample?

12_ A sample has a mean M = 50. In the sample, a score of X = 41 corresponds to z = -1.50. What is the standard deviation for the sample?



Answers

A sample has a mean of 50 and a standard deviation of $4.0 .$ Find the $z$ -score for each value of $x$ : a. $x=54$ b. $x=50$ c. $x=59$ d. $x=45$

In this problem were asked to find the standard deviation of a some and we're given that mu of X is 12. That sickness of X is one and that the sample size is 25 in order to calculate the standard deviation of a some that is equal to the product of the square root of the sample size times sickness of acts. So in this instance, it's the square 25 times one which is equal to five.

Okay, so we know that the population has a mean she called to 1 15. I standard deviation signal equal to 25 in sample size of 50. So sample sizes good than 30. So we can use the central limit term to conclude that the distribution of sample means is approximately normal with the mean on the standard deviation. Both muse X. I mean, I see myself x physical, too show. And yeah. So this is therefore equal to 1 50. This is equal to 25. 50. Because you have put flesh. Sure. So we're screwed. Oh, contract should be Tom. Yeah. 2.5 36

So we are looking for the X value. Usually we're looking for the Z value, we're going to use the same formula and we know Z equals negative 1.2, we're looking for X. The mean is 2.3 and the median is 1.3 or the standard deviation is 1.3. Excuse me. So we're going to do mhm 1.2 times 1.3 And that's going to give us 1.56 and it's going to be negative negative 1.56 equals X -2.3. So we're going to add 2.3 to both sides. So we get oh uh huh, -1.56 Plus 2.3 And that equals .74 equals X. Uh huh. Yeah.

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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