# Math Help - Z-Scores and Standard Deviation Help

1. ## Z-Scores and Standard Deviation Help

Hey, I'm new to this forum. I just started studying psychology and I haven't quite grasped the workings of z-scores. In an exercise, I have to answer the following question:

A score that is 20 points above the mean corresponds to a z-score of z = +2. What is the standard deviation?

It's probably a very simple question, but I've blanked out. Could someone please explain to me how the answer is achieved?

Another one I'm confused about... For a population with σ = 12, a score of X = 87 corresponds to z = -0.25. What is the mean for this distribution?

2. Originally Posted by Gwame
Hey, I'm new to this forum. I just started studying psychology and I haven't quite grasped the workings of z-scores. In an exercise, I have to answer the following question:

A score that is 20 points above the mean corresponds to a z-score of z = +2. What is the standard deviation?

It's probably a very simple question, but I've blanked out. Could someone please explain to me how the answer is achieved?

Another one I'm confused about... For a population with σ = 12, a score of X = 87 corresponds to z = -0.25. What is the mean for this distribution?
You should know $Z = \frac{X - \mu}{\sigma}$. Therefore:

1) $2 = \frac{(\mu + 20) - \mu}{\sigma}$. Solve for $\sigma$.

2) $-0.25 = \frac{87 - \mu}{12}$. Solve for $\mu$.

3. Originally Posted by Gwame
Hey, I'm new to this forum. I just started studying psychology and I haven't quite grasped the workings of z-scores. In an exercise, I have to answer the following question:

A score that is 20 points above the mean corresponds to a z-score of z = +2. What is the standard deviation?

It's probably a very simple question, but I've blanked out. Could someone please explain to me how the answer is achieved?

Another one I'm confused about... For a population with σ = 12, a score of X = 87 corresponds to z = -0.25. What is the mean for this distribution?
Different set of samples have different mean values. The mean value is the center point of all numbers in the set. Different set of data have different mean values, and different means give different center point, which means that every time when you have a set of samples, you need to plot a different graph for the probability distribution, but all these extra work is unnecessary if you could standardize it. Once you standard it, you can use the same graph repeatedly. The standardized mean is always zero, and the standard deviation is measured a distance from zero. The distance from zero is the standard deviation of the set of data. Say the average of height all your chairs is 3 feet, plus and minus 3 inches. The plus and minus is the deviation. This can be 1 standard deviation or 0.5 standard deviation. 1 is further from the center than 0.5. The z-score tells you the distance from the center point of you data; it’s directly related to the sample mean and standard deviation.

4. Originally Posted by mr fantastic
You should know $Z = \frac{X - \mu}{\sigma}$. Therefore:

1) $2 = \frac{(\mu + 20) - \mu}{\sigma}$. Solve for $\sigma$.

2) $-0.25 = \frac{87 - \mu}{12}$. Solve for $\mu$.
Thanks for your reply. So in the first question, can I cancel out the two $\mu$s, leaving 2 = 20/ $\sigma$, therefore $\sigma$ = 10? And the second question, answer = 90?

5. Originally Posted by Gwame
Thanks for your reply. So in the first question, can I cancel out the two $\mu$s, leaving 2 = 20/ $\sigma$, therefore $\sigma$ = 10? And the second question, answer = 90?
Yes.

CB

Many thanks.