x Turn on thread page Beta
 You are Here: Home >< Maths

# z-scores watch

1. Regarding z-scores, how would I do the following questions? Have no idea and google isn't so helpful.
1) Find the proportion of a normaldistribution that is located between the z-score boundaries listed:a)
a) Between z = -0.5 and z = + 0.5b) b) Between z = -1 and z = +1c) c) Between z = -1.96 and z = +1.96
2) For a normaldistribution with a mean of 100 and an SD of 20, what score separates the top40% from the bottom 60%?
2. (Original post by Juuuuh)
Regarding z-scores, how would I do the following questions? Have no idea and google isn't so helpful.
1) Find the proportion of a normaldistribution that is located between the z-score boundaries listed:a)
a) Between z = -0.5 and z = + 0.5b) b) Between z = -1 and z = +1c) c) Between z = -1.96 and z = +1.96
2) For a normaldistribution with a mean of 100 and an SD of 20, what score separates the top40% from the bottom 60%?
Have you tried graphing the normal distribution and interpreting the table values as certain areas under the normal distribution? The total area under the curve is 1.

Also, the graph is symmetrical so -0.5 to +0.5 is the same thing as finding the 0 to 0.5 and doubling that.
3. (Original post by Zacken)
Have you tried graphing the normal distribution and interpreting the table values as certain areas under the normal distribution? The total area under the curve is 1.

Also, the graph is symmetrical so -0.5 to +0.5 is the same thing as finding the 0 to 0.5 and doubling that.
I don't really know what you mean because I've never really done this stuff before!

I have my distribution table in a book. I just don't understand the graph stuff/how to find the proportion of normal distribution
4. (Original post by Juuuuh)
I don't really know what you mean because I've never really done this stuff before!

I have my distribution table in a book. I just don't understand the graph stuff/how to find the proportion of normal distribution
So, given a z score of say 0.5, the table value of z=0.5 gives you the area under the curve from z=-ve infinity to z=0.5 or 1-(area between z=0.5 and z=infinity)/

The area from z=-ve infinity to z=0 is 1/2 so the area from z=0 to 0.5 is the table value of z=0.5 minus 1/2, then double this to get the area between -0.5 to 0.5, or the proportion of the curve you want.

Can you do this for the other z values?
5. (Original post by Zacken)
So, given a z score of say 0.5, the table value of z=0.5 gives you the area under the curve from z=-ve infinity to z=0.5 or 1-(area between z=0.5 and z=infinity)/

The area from z=-ve infinity to z=0 is 1/2 so the area from z=0 to 0.5 is the table value of z=0.5 minus 1/2, then double this to get the area between -0.5 to 0.5, or the proportion of the curve you want.

Can you do this for the other z values?
Ah right so you find the value which corresponds to 0.5 on the table and then double that to get the percentage? I think I understand that now, thank you.

What about a question like this? For a normal distribution with a mean of 100 and an SD of 20, what score separates the top 40% from the bottom 60%?

Sorry for all of the questions, ha.
6. (Original post by Juuuuh)
Ah right so you find the value which corresponds to 0.5 on the table and then double that to get the percentage? I think I understand that now, thank you.

What about a question like this? For a normal distribution with a mean of 100 and an SD of 20, what score separates the top 40% from the bottom 60%?

Sorry for all of the questions, ha.
Well, not really.

If you find the value that corresponds to 0.5 on the table, you'll get the area from -ve infinity to 0.5, you want just the area from 0 to 0.5, you need to take the value that corresponds to 0.5, subtract 1/2 from that value THEN double it.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 3, 2015
Today on TSR

### University rankings 2019

Cambridge at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams