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

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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.

• 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?

— Fly by Night (talk) 00:19, 3 January 2011 (UTC)

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)