# Normal Distribution Question

#### latonya1

##### New Member
Need Help!!!
Here is the problem:

The National Center for Educational Statistics report that in the year ending 2003 some 400,000 students took the Graduate Record Examination. For this set of examinees, the observed mean Quantitative Score was 560 with a Standard Deviation (SD) of 100.

Assuming the distribution is normal, determine:

1. The number of students below/above the mean score.
2. The number of students whose scores fall between 1SD below the mean and 1SD above the mean.
3. The number of students whose scores will be less than 2SD above the mean.
4. Percentile rank of student who scores 760 in the Quantitative exam.
5. What is the score for a student whose score in the Quantitative exam is 1SD above the mean. What is her score.

Please help!! What is the formula for determining these scores. This is my first Graduate Statistical course in almost 10 years. I would appreciate any help. I just need some direction.
Thank you,
latonya #### latonya1

##### New Member
Normal distribution

I have figured out the the number of students whose scores fall between 1SD below the mean and 1SD above the mean.

68% of 400,000= 272,000
400,000-272,000= 128,000

I also figured out the score that would be 1SD above the mean= 660

I still need to figure out the number of students below/above the mean score

Latonya

#### Xenu

##### New Member
I still need to figure out the number of students below/above the mean score
hint: You know that the distribution is symmetric around it's mean, so...

#### latonya1

##### New Member
I still don't get it. Please give another hint.
Please give me some direction for #3 as well.
Thanks,
latonya

#### latonya1

##### New Member
normal distribution

latonya

#### edtecher

##### New Member
so...if the mean is basically the average, how many students out of 400k would fall on either side?

and for #3, it would include EVERYONE below 2 SD above the mean...what's the percentage of 2 SD?

#### latonya1

##### New Member
normal distribution

The percentage of 2SD is 95%. 95% of 400,000 is 20,000.

So would the number of students be 380,000 less than 2SD above the mean?

Would 200,000 students fall below the mean and 200,000 fall above the mean?

latonya

#### latonya1

##### New Member
Distribution

Am i on the right track?

Latonya

#### Xenu

##### New Member
The percentage of 2SD is 95%. 95% of 400,000 is 20,000.

So would the number of students be 380,000 less than 2SD above the mean?
This is not correct. As stated before you are looking for everyone that is below 2SD above the mean. 95% is (roughly) the percentage that lies between -2SD and +2SD from the mean. So in your calculations, you exclude everyone that is below -2SD from the mean.

Do you have a table over the standard normal distribution that you use to get your numbers?

Would 200,000 students fall below the mean and 200,000 fall above the mean?
Correct.

#### latonya1

##### New Member
So the answer would then be 20,000 students would be less than 2SD above the mean.

latonya

#### Xenu

##### New Member
So the answer would then be 20,000 students would be less than 2SD above the mean.
No, that answer wouldn't make any sense at all, does it?

What I was trying to say is that you are not trying to find the number of students between -2 and 2 SD (which is how you got the 95%). You are trying to find the number of students between +2SD and minus infinity.

#### latonya1

##### New Member
I understand that, but How do I do that? What is the process? How do I compute that? That is what I am asking.

latonya

#### Xenu

##### New Member
You can use a table over the standard normal distribution to find the area below 2 SD. This area represent the fraction of the students. Then multiply by the number of students as you have done in the previous tasks.

#### latonya1

##### New Member
Would that be the table that shows the percentage of each standard deviation? Once I get that fraction, would I then multiply it by 380,000? I am stomped on this. It is probably very simple to you but I don't get it. I had this question as a homework question and I could not figure it out, so I left it blank. I would still like to know how to compute it.

Someone help!
latonya