# Thread: Normal Distribution (z scores)

1. ## Normal Distribution (z scores)

Hi,

I am revising for my final Maths exam ever on Monday. I am struggling with some questions on my revision sheet in relation to finding means and standard deviations in these problems. For example, here are a few of the questions from my revision sheet:

11. What is the mean of a normal distribution which has a standard deviation of 5 and in which a raw score of 30 corresponds to a standard score of 1.7?

12. In a normal distribution, the standard deviation is 2.3 and a score of 62 corresponds to a standard score of -0.5. What is the mean of the distribution?

13. What are the mean and the standard deviation of a normal distribution when raw scores of 45 and 60 correspond to stand scores of -1 and 2 respectively?

14. In a normal distribution scores of 70 and 50 correspond to standard scores of 01.5 and -1.5 respectively. Calculate the mean and standard deviation of the distribution.

It would be great if somebody could give me the formulas to solve these questions or any tips on the subject. Bare in mind we are using very basic scientific calculators.

Thanks.

2. Originally Posted by Calslappy
Hi,

I am revising for my final Maths exam ever on Monday. I am struggling with some questions on my revision sheet in relation to finding means and standard deviations in these problems. For example, here are a few of the questions from my revision sheet:

11. What is the mean of a normal distribution which has a standard deviation of 5 and in which a raw score of 30 corresponds to a standard score of 1.7?
Recall that the z score is defined as $z=\frac{x-\bar{x}}{s}$

In this problem, $z=1.7$, $x=30$ and $s=5$. Do you think that you can find $\bar{x}$ now?

12. In a normal distribution, the standard deviation is 2.3 and a score of 62 corresponds to a standard score of -0.5. What is the mean of the distribution?
Similar to problem #11

13. What are the mean and the standard deviation of a normal distribution when raw scores of 45 and 60 correspond to stand scores of -1 and 2 respectively?
This is a little different, but has the same idea. This time, though, we will have to solve a system of equations.

One equation is $-1=\frac{45-\bar{x}}{s}\implies \bar{x}-s=45$

The other equation is $2=\frac{60-\bar{x}}{s}\implies \bar{x}+2s=60$

Thus, our system that we need to solve is $\left\{\begin{array}{rcrcr}\bar{x}&-&s&=&45\\\bar{x}&+&2s&=&60\end{array}\right.$

Can you take it from here?

14. In a normal distribution scores of 70 and 50 correspond to standard scores of 01.5 and -1.5 respectively. Calculate the mean and standard deviation of the distribution.
Similar to problem #13.

It would be great if somebody could give me the formulas to solve these questions or any tips on the subject. Bare in mind we are using very basic scientific calculators.

Thanks.
Does this make sense?

--Chris

3. Yes it does. Thank you