What percentage of the data is withing 2.5 standard deviations of the mean?

Question

I know what 1, 2, and 3 is, but I have scoured far and wide and not found 2.5.

Answer 1

Hi Jack,

Assuming you mean data in a standard normal distribution, you can get this from a z-score table, I cannot link here as Wyzant reviews posts with links, but you can find one with a standard Internet search. Effectively, your z-score is 2.5, so look that value up to get the corresponding probability:

P (Z<2.5)=0.9938

But we’re not done yet—remember that the distribution is two-sided, so we also must look up z-score negative 2.5:

P(Z< -2.5)=0.0062

Essentially, we want the area between these two values, so:

P=0.9938 - 0.0062 = 0.9876 =

98.76%

I hope this helps.