Below is the syntax highlighted version of Sampling.java
from §2.1 Static Methods.

/****************************************************************************** * Compilation: javac Sampling.java * Execution: java Sampling n p * * Suppose that p = 40% of the population favors candidate A. If we take a * random sample of n = 200 voters, what is the probability that less than * half the voters support candidate A? * * The number X of the n = 200 voters that support candidate A is binomial * distributed with mean n * p = 200 * 0.4 = 50 and variance * n * p * (1 - p) = 200 * 0.4 * 0.6 = 48. The standard deviation is * The probability that less than half the voters support candidate A is * the probability that X < n / 2 = 100. * * Using the normal approximation to the binomial distribution, the * probability that X < 100 is: * P(Z <= (100-80) / sqrt(48)) = P (Z <= 2.886) * * ******************************************************************************/ public class Sampling { public static void main(String[] args) { int n = Integer.parseInt(args[0]); double p = Double.parseDouble(args[1]); double prob = Gaussian.Phi((0.5*n - p*n) / Math.sqrt(n*p*(1-p))); StdOut.println("probability = " + prob); } }

Last updated: Thu Aug 11 10:15:13 EDT 2022.