Day 5: Normal Distribution I HackerRank Solution

Day 5: Normal Distribution I HackerRank Solution
Source : https://www.hackerrank.com/challenges/s10-normal-distribution-1

Objective
In this challenge, we learn about normal distributions. Check out the Tutorial tab for learning materials!

Task
In a certain plant, the time taken to assemble a car is a random variable, , having a normal distribution with a mean of hours and a standard deviation of hours. What is the probability that a car can be assembled at this plant in:

1. Less than hours?
2. Between and hours?

Input Format

There are lines of input (shown below):

20 219.520 22

The first line contains space-separated values denoting the respective mean and standard deviation for . The second line contains the number associated with question . The third line contains space-separated values describing the respective lower and upper range boundaries for question .

If you do not wish to read this information from stdin, you can hard-code it into your program.

Output Format

There are two lines of output. Your answers must be rounded to a scale of decimal places (i.e., format):

1. On the first line, print the answer to question (i.e., the probability that a car can be assembled in less than hours).
2. On the second line, print the answer to question (i.e., the probability that a car can be assembled in between to hours).

Source : https://www.hackerrank.com/challenges/s10-normal-distribution-1

Solution

	// github.com/RodneyShag
	public class Solution {
	public static void main(String[] args) {
	double mean = 20;
	double std = 2;
	System.out.format("%.3f%n", cumulative(mean, std, 19.5));
	System.out.format("%.3f%n", cumulative(mean, std, 22) - cumulative(mean, std, 20));
	}
	/* 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;
	}
	}