Z-score cumulative probability??

[Crys]

Hi! My question isn't about any particular homework problem, just a general knowlede question! I was wondering, what is the formula for finding the cumulative probability of a z-score (i.e., area under the curve left of the z-score)? I'm guessing the formula displayed on this chart - http://business.statistics.sweb.cz/normal01.jpg - IS that formula, but I have no idea how io interpret it. Thank you for any response or clue you can give!

 

[galactus]

Yes, that is the formula.

The formula for finding those values in a z table is:

\(\displaystyle \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{z}e^{\frac{-t^{2}}{2}}}dt\)

This can not be evaluated by elementary means. It is known as the 'error function'.

The best thing to do is use some sort of tech to evaluate it for some particular z score.

Compare to a z table. Let z=0.

\(\displaystyle \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{0}e^{\frac{-t^{2}}{2}}}dt=.50\)

 

[Crys]

Hrm, thank you! I know it's probably above what I can do, and that I don't need to do it, but I was hoping for some explanation, even in overly-simple terms on the general idea behind it. I guess considering the literature I've found on it, it can't be dumbed down like that. I appreciate your help though!