Wikipedia:Reference desk/Archives/Mathematics/2011 January 3

= January 3 =

Percentages and Probability
Let's say you hold an election and the sample size is s1. You achieve an approval rating of A%. Then, you analyse the results from randomly selected subsets of the electorate. Assume that you randomly selected s2 people and they tell you how they actually voted. — Fly by Night  ( talk )  00:19, 3 January 2011 (UTC)
 * What is the probability of getting an approval rating of A% in this smaller sub-sample?
 * What is the probability of the approval rating being within ±d% of the original approval rating?
 * If you want an exact result, you need to sum the values of the Hypergeometric distribution. Note that if $$s_1$$ and $$s_2$$ are coprime and $$0<A<1$$, then the probability of having exactly A is 0.
 * For an approximation, you can use the normal distribution with $$\mu=A$$ and $$\sigma=\frac{A(1-A)}{s_2}$$. -- Meni Rosenfeld (talk) 09:25, 3 January 2011 (UTC)
 * Thanks for that Meni. — Fly by Night  ( talk )  15:13, 3 January 2011 (UTC)