z-score Calculus Example

[Jason76]

What would be a simple example of finding a z-score using Calculus? I do know about the other way

\(\displaystyle z = \dfrac{x - \mu}{\sigma}\)

Then you look up the percentage value form a z-score table. Next, you add that to \(\displaystyle 0.5\). Next you subtract this whole value from 1.0 to find the rest of the bell curve.

 

[stapel]

I'm not sure what you mean by your question. But the integral formulation is listed, for instance, here.

 

[Jason76]

Post Edited.

Let's say I gotta z-score of -1 and t value of 10

I guess the first move is to substitute -1 for z in the integral sign But how to integrate that e expression

 

[Jason76]

http://en.wikipedia.org/wiki/Error_function

Interesting, but which one would help us find "table values" assuming we did not have access to a table. For instance, we get a z-score of something, and then we need to look up a table, but have no access to one.

 

[Jason76]

Nice tutorial here:

http://www.zweigmedia.com/RealWorld/cprob/cprob2.html

http://infohost.nmt.edu/~olegm/484/Chap2.pdf

I understand the first problem there, but not the second one where it's evaluated at x and 0.

 

[Jason76]

Finding the probability, using Calculus is fairly straightforward. However, one must know the curve's equation (\(\displaystyle y = 5x^{2} + 4\) etc...) Of course, in non-calc statistics, we do NOT know the equation; Therefore we have to resort to a z-score.