# Thread: standard deviation

1. ## standard deviation

For a standard normal distribution what percentage of data is more than 2 standard deviations away from the mean?

I can do every other problem except this one, help me understand it please.

2. Originally Posted by sneze57
For a standard normal distribution what percentage of data is more than 2 standard deviations away from the mean?

I can do every other problem except this one, help me understand it please.
By the empirical rule, we know roughly 95% of data lies within 2 standard deviations of the mean. Thus, that would mean that 5% lie within more than 2 standard deviations from the mean.

Does this make sense?

3. I understand that, what doesn't make sense is that in the back of the book the answer is 4.55%. Why is that?

4. Originally Posted by sneze57
I understand that, what doesn't make sense is that in the back of the book the answer is 4.55%. Why is that?
Because you used a rule-of-thumb rather than doing a more exact calculation.

Pr(Z > 2) = 0.02275 therefore the percentage of data that's more than $2 \sigma$ from $\mu$ is 2(0.02275)(100) = 4.55 % (correct to two decimal places).

5. wow ok, where are you getting .02275 from? Could you explain how you got there a little more.

6. Originally Posted by sneze57
wow ok, where are you getting .02275 from? Could you explain how you got there a little more.
To get this answer you need to either know how to use the Standard Normal Tables, or use technology.

7. You come on the math help forum and tell me to figuare it out for myself?

8. Originally Posted by sneze57
You come on the math help forum and tell me to figuare it out for myself?
I have shown you where the answer comes from and suggested two ways of how to get it. From your response it appears that you have not been taught how to answer a question like this, in which case you need to discuss it with your instructor rather than blaming me.

9. Mr. fantastic, next time why don't you just answer the question a little better.

10. Originally Posted by sneze57
Mr. fantastic, next time why don't you just answer the question a little better.
If you'd cooperated by saying how you'd been taught to calculate probabilities for a normal distribution (tables, technology etc.) the help you needed could have been better given.

If you have anything productive to say you can pm me. Thread closed.