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Approximating binomial probabilities with Stirling

By markhuber in Binomial on September 28, 2012.

Let \(X\) be a binomially distributed random variable with parameters \(n = 1950\) and \(p = 0.342\).

(a) Approximate \(\mathbf{P}(X = 700)\) using Stirling’s approximation to eight significant digits.

(b) Find \(\mathbf{P}(X = 700)\) exactly to eight significant digits using Wolfram Alpha.

[Author Mark Huber. Licensed under Creative Commons.]

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