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.
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 $\displaystyle 2 \sigma$ from $\displaystyle \mu$ is 2(0.02275)(100) = 4.55 % (correct to two decimal places).
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.
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.