# statistics: standard deviation normal curve

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#### DrPettans

##### Full Member

In a normal distribution curve, what percent of the cases are ABOVE 1 standard deviation BELOW the mean??
The book says it's 84% but I do not understand why. I'd have answered 34% based on this knowledge:

within 1SD there's 68% of the cases (34% are -1SD + 34% that are +1SD)
within 2 SD there's 95% of the cases (47,5% + 47,5%)
within 3 SD there's 99.7% of the cases (49.85% + 49.5%)

1SD BELOW the mean is -1SD which is 34%, and it says that it is ABOVE that. Therefore, my answer would be 34%.

Why am I wrong, if I am?

#### DrPettans

##### Full Member
Also, another question says:
A student scores at the 97.5 percentile. That falls where on the curve?? It says 2SD ABOVE the mean... but I think it would be more correct to say he is ABOVE 2SD ABOVE the mean, or BETWEEN 2 and 3 SD ABOVE the mean, because 97.5 is between 95% (2SD) and 99.7% (3SD). What do you think?
Thank you guys.

#### DrPettans

##### Full Member
In a normal distribution curve, what percent of the cases are ABOVE 1 standard deviation BELOW the mean??
The book says it's 84% but I do not understand why. I'd have answered 34% based on this knowledge:

within 1SD there's 68% of the cases (34% are -1SD + 34% that are +1SD)
within 2 SD there's 95% of the cases (47,5% + 47,5%)
within 3 SD there's 99.7% of the cases (49.85% + 49.5%)

1SD BELOW the mean is -1SD which is 34%, and it says that it is ABOVE that. Therefore, my answer would be 34%.

Why am I wrong, if I am?

Ok editing this one, i understood now. It asks for ALL THE VALUES above 1 sd below the mean, which would be 34% (from -1sd to the mean) + the other 50% above the mean.

#### DrPettans

##### Full Member
But i still don't get the second one, about the student percentile

#### Silverish

##### Full Member
In a normal distribution curve, what percent of the cases are ABOVE 1 standard deviation BELOW the mean??
The book says it's 84% but I do not understand why. I'd have answered 34% based on this knowledge:

within 1SD there's 68% of the cases (34% are -1SD + 34% that are +1SD)
within 2 SD there's 95% of the cases (47,5% + 47,5%)
within 3 SD there's 99.7% of the cases (49.85% + 49.5%)

1SD BELOW the mean is -1SD which is 34%, and it says that it is ABOVE that. Therefore, my answer would be 34%.

Why am I wrong, if I am?
68% + 16% = 84%
Think of the bell curve and consider the horizontal line 1 SD below from the mean. That line represents the SD below the mean. The question is asking for the percentage above that line.

For the second question, I think you're right. But I also think you're overthinking it.
A lot of times its the BEST ANSWER. Not always the exact answer. It's really annoying but its something we all have to deal with.

#### tasar1898

##### Full Member
2 SD above mean = > mean + 2SD , its just their ''terminology'' ...

#### DrPettans

##### Full Member
Thank you again, partner