Probability and Binomial and Chi tests - Help

Hi,

I made a survey to n people asking their sign (12 signs were available).

A number k answered Libra. I want to analyze this result. But I'm not
sure if I'm doing it right. First I assume:

p = 1/12
q = 1 - p

Then the Binomial probability is:

PROB = nCk * p^k * (1-p)^(n-k)

The Binomial Test is:

z = (k/n-p)/sqr(p*q/n)

and the Chi-Squared is:

X^2 =(k - p * n) ^ 2 / (p * n) + ((n - k) - q * n) ^ 2 / (q * n)


Am I right?

I'm not sure about the value of p in the Binomial Test (should it be = PROB?), and if the Chi-squared can be calculated like that.

Kind regards,

Kepler