# Normal Distribution

#### sceater

##### New Member
I cant figure out how to do this problem: I have 2 sets of means and 2 sets of SD

1sth graders scored a mean of 25 and a sd of 5
5th graders scored a mean of 30 and an sd of 10; assume the distributions are normal

How do i figure out what percentage of the first graders scored better than the average 5th graders?

i did (30-25)/5 which gives me 1; the z-score percentile i get is 15.57% (smaller portion) but i dont think thats how you do it.

The second question asks which percentage of fifth graders scored lower than the average 1st grader. But I will end up getting the same answer if i do it the same...

#### Dason

the z-score percentile i get is 15.57% (smaller portion) but i dont think thats how you do it.
Seems fine to me
The second question asks which percentage of fifth graders scored lower than the average 1st grader. But I will end up getting the same answer if i do it the same...
Will you? Give it a try.

#### Dason

No. I'm saying do the actual calculation for the second one. Like forget about anything to do with the first problem and do the second problem.

#### sceater

##### New Member
No. I'm saying do the actual calculation for the second one. Like forget about anything to do with the first problem and do the second problem.
so would it be (25-30)/10? which would give me -.50 which is .3825?

#### Dason

so would it be (25-30)/10? which would give me -.50 which is .3825?
Well -.50 isn't .3825. Be careful when you say stuff like this - it will cause graders to want to take away all of your points. Also that isn't the correct probability calculation even though it's the correct z-value.

#### sceater

##### New Member
Well -.50 isn't .3825. Be careful when you say stuff like this - it will cause graders to want to take away all of your points. Also that isn't the correct probability calculation even though it's the correct z-value.
what would the correct probability be? I thought it would be 38.25% since that is one of the tails and I want to look at the percentage of students that scored lower than 25. Or most likely im seeing/understanding it wrong...any guidance?

#### Dason

Are you absolutely sure that is the correct tail probability? Why don't you check again.

#### sceater

##### New Member
Are you absolutely sure that is the correct tail probability? Why don't you check again.
would it be .6915 then? if so why? in the z table I see..

Mean to z: .1915 Larger portion .6915 Smaller portion .3085