# Variance/Normal Distributions

#### shae13v

##### New Member
I am currently in a psych tests and measurements class. I have a couple of questions that I can't figure out or find in the book.
They are multiple choice questions.

1. If a raw score of 80 equals a z score of 2.00 in a distribution of scores with M=50, then the variance must equal?
A. 30
B. 60
C. 160
D. 225

2. If Test X has a mean of 50, standard deviation of 10 (assuming a normal distribution), and N=1000. How many individuals score between 40 and 60?
A. 340
B. 680
C. 990

Any help is appreciated. I would really like to see your work on how you come up with the answer so I can try to learn how to do it myself.

Thanks!

#### JohnM

##### TS Contributor
1. z = (x - mu)/s

z = 2.00
x = 80
mu = 50

Solve for s, then square it to get the variance.

2. Use the normal distribution tables to determine what percentage of the standard normal curve falls between 40 and 60 (convert these to z scores first). Then multiply that percentage by 1000 (sample size).
--> We have a post in the Examples section that explains how to find areas under the normal curve

#### shae13v

##### New Member
Still a question

Thank you for helping. I have figured out #1 but I'm still having trouble with the normal distribution question.
Any further help?

#### JohnM

##### TS Contributor
mu = 50
s = 10

x1 = 60
x2 = 40

z = (x - mu)/s
z1 = (60 - 50)/10 = 1.0
z2 = (40 - 50)/10 = -1.0

Now find the proportion of the area under the standard normal curve between z scores of 1.0 and -1.0. Once you find this area (use the normal distribution tables - the post in the Examples section entitled "The Vaunted Normal Distribution" explains how), multiply it by 1000, and you'll get the number of people who score between 40 and 60.

#### shae13v

##### New Member

Thank you so much! I really appreciate the help. I have completed those problems.

I have 2 more if you don't mind helping. I have completed all 46 other problems on my own (I saw that you only help those who are putting in an effort.)

1. How do you determine what will happen to the standard error of measurement if the standard deviation of a set of test scores increases but the reliability remains constant?

2. On a test whose distribution is approximately normal with a mean of 50 and a standard deviation of 10:
Learner A has a raw score of 65
Learner B has a percentile rank of 70
Learner C has a standard score of 1.00

What is the rank order of these learners from high to low?

A. ABC
B. ACB
C. BAC
D. CAB

#### JohnM

##### TS Contributor
1. hint: if either one of those measurements change, the std error of measurement will change

2. using mu=50 and sd=10, convert the information given for students A,B,C into the same thing, either raw scores, standard scores (z scores), or percentile ranks (area under the curve) and simply rank order them.

• standard score = (raw score - mu)/sd
• percentile rank = percentage of the area under the normal curve between negative infinity and the standard score

#### shae13v

##### New Member

Is there a way (formula) to determine if the standard error of measurement will increase or decrease?

#### JohnM

##### TS Contributor
it will move in the same direction as the standard deviation

#### shae13v

##### New Member

Is that just a rule or is there some sort of formula to apply?

#### shae13v

##### New Member
Thank you!

I really can't thank you enough. You've been very helpful and I appreciate it!
If I lived nearer to you, you would definitely have a full-time tutoring student Thanks again!

#### coco

##### New Member
Problems with this exericise

Hi,

I am struggling with this exercise you posted some time ago. My problems is with the percentile....I am not able to see how to related to the other two.