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# Stats: Z scores and normal distributions watch

1. I'm really confused on how to go about questions which are something like:

What is the percentage of scores which were below 2 SD

How do I work this out?

Thank you
2. (Original post by LeaX)
I'm really confused on how to go about questions which are something like:

What is the percentage of scores which were below 2 SD

How do I work this out?

Thank you
It might be useful to know that 68% of the distribution lies within one standard deviation of the mean. 95% of the distribution lies within two standard deviations and 99.7% of the distribution lies within three standard deviations of the mean.
It might be useful to know that 68% of the distribution lies within one standard deviation of the mean. 95% of the distribution lies within two standard deviations and 99.7% of the distribution lies within three standard deviations of the mean.
So does 95% lie between -2 SD and +2 SD? How would I work out how many are below 2SD?
4. (Original post by LeaX)
So does 95% lie between -2 SD and +2 SD? How would I work out how many are below 2SD?
Correct. Do you have an example of a question handy? It'll be easier to explain with one.
5. let's say you want to work out the value of the interval that contains 95% of the data and is centered around the mean

clearly, there is 5% missing overall, so each tail will be 2.5% and the values you are looking for are 47.5% on either side

using the reverse probability tables and the symmetry of the distribution, we can look up the z values for a probability of 47.5% either side and find out that they give about 1.96, so the number of standard deviations away from the mean that contain 95% of the data is about 1.96 (using for our intervals)

hope this helps
Correct. Do you have an example of a question handy? It'll be easier to explain with one.
Not a specific one, we were just told we'd need to know how to interpret questions like that using this kind of graph:

(Original post by Arithmeticae)
let's say you want to work out the value of the interval that contains 95% of the data and is centered around the mean

clearly, there is 5% missing overall, so each tail will be 2.5% and the values you are looking for are 47.5% on either side

using the reverse probability tables and the symmetry of the distribution, we can look up the z values for a probability of 47.5% either side and find out that they give about 1.96, so the number of standard deviations away from the mean that contain 95% of the data is about 1.96 (using for our intervals)

hope this helps
Thank you. I think I understand now. Can I just ask one question - is standard deviation and z scores quantitively the same thing (I know they have different units) but will 1 SD always be equal to 1 (whatever the units of the DV)

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Updated: December 1, 2014
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