Solution.java

// github.com/RodneyShag

public class Solution {
    public static void main(String[] args) {
        double mean = 70;
        double std  = 10;
        
        double result_1 = 100 * (1 - cumulative(mean, std, 80));
        double result_2 = 100 * (1 - cumulative(mean, std, 60));
        double result_3 = 100 * cumulative(mean, std, 60);
            
        System.out.format("%.2f%n", result_1);
        System.out.format("%.2f%n", result_2);
        System.out.format("%.2f%n", result_3);
    }
    
    /* Calculates cumulative probability */
    public static double cumulative(double mean, double std, double x) {
        double parameter = (x - mean) / (std * Math.sqrt(2));
        return (0.5) * (1 + erf(parameter));
    }
        
    /* Source: http://introcs.cs.princeton.edu/java/21function/ErrorFunction.java.html */
    // fractional error in math formula less than 1.2 * 10 ^ -7.
    // although subject to catastrophic cancellation when z in very close to 0
    // from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2
    public static double erf(double z) {
        double t = 1.0 / (1.0 + 0.5 * Math.abs(z));

        // use Horner's method
        double ans = 1 - t * Math.exp( -z*z   -   1.26551223 +
                                            t * ( 1.00002368 +
                                            t * ( 0.37409196 + 
                                            t * ( 0.09678418 + 
                                            t * (-0.18628806 + 
                                            t * ( 0.27886807 + 
                                            t * (-1.13520398 + 
                                            t * ( 1.48851587 + 
                                            t * (-0.82215223 + 
                                            t * ( 0.17087277))))))))));
        if (z >= 0) return  ans;
        else        return -ans;
    }
}