Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    3
    ReputationRep:
    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%?
    Offline

    22
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (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
    Offline

    22
    ReputationRep:
    (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?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (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.
    Offline

    22
    ReputationRep:
    (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.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 3, 2015
Poll
Do you like carrot cake?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.