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z-scores

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%?
Reply 1
Avatar for Zacken
Zacken
22
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.
Reply 2
Avatar for Juuuuh
Juuuuh
OP
5
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! :frown:

I have my distribution table in a book. I just don't understand the graph stuff/how to find the proportion of normal distribution
Reply 3
Avatar for Zacken
Zacken
22
Original post by Juuuuh
I don't really know what you mean because I've never really done this stuff before! :frown:

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?
Reply 4
Avatar for Juuuuh
Juuuuh
OP
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.
Reply 5
Avatar for Zacken
Zacken
22
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.

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