HackerRank Day 6: The Central Limit Theorem I | 10 Days of Statistics solution

In this Hackerrank Day 6: The Central Limit Theorem I 10 Days of Statistics problem A large elevator can transport a maximum of 9800 pounds. Suppose a load of cargo containing 49 boxes must be transported via the elevator. The box weight of this type of cargo follows a distribution with a mean of 205 pounds and a standard deviation of 15 pounds. Based on this information, what is the probability that all 49 boxes can be safely loaded into the freight elevator and transported?

Problem solution in Python programming.

# Enter your code here. Read input from STDIN. Print output to STDOUT
import math

x = int(input())
n = int(input())
mu = int(input())
sigma = int(input())

mu_sum = n * mu 
sigma_sum = math.sqrt(n) * sigma

def cdf(x, mu, sigma):
    Z = (x - mu)/sigma
    return 0.5*(1 + math.erf(Z/(math.sqrt(2))))

print(round(cdf(x, mu_sum, sigma_sum), 4))

Problem solution in Java Programming.

import java.io.*;
import java.util.*;

public class Solution {
    public static double erf(double z, double x)
    {
        int direction = z>0?1:-1;
        double result =0;
        double delta = .000001;
        double iz = 0;
        while(iz*direction<z*direction) {
            result+=delta*Math.pow(Math.E,-(iz*iz))*direction;
            iz+=delta*direction;
        }
        //System.out.printf("result=%.5f\n",result);
        return 2./Math.sqrt(Math.PI) * result;
    }
    public static double normal_dist_func(double x, double mu, double stddev)
    {
        double z = ((x-mu)/(stddev*Math.sqrt(2)));
        //System.out.println("z=" +z + ", " + "erf=" + erf(z,x));
        return .5*(1+erf(z,x));
    }
    
    public static void main(String[] args) {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        double mean = 205*49;
        double stddev = 15*Math.sqrt(49);
        System.out.printf("%.4f\n",normal_dist_func(9800,mean,stddev));
    }
}

Problem solution in C++ programming.

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

double phi(double x){
    return (exp(-x*x*0.5)/sqrt(2*M_PI));
}

double normal(double mean, double sigma, double x){
    return phi((x-mean)/sigma)/sigma;
}

double erf(double x){
    int n = 100;
    double dt = x / n;
    double sum = 0;
    for (int i = 0; i < n; i++){
        double z = i * dt + 0.5 * dt;
        sum += exp(-z * z) * dt;
    }
    return sum * 2 / sqrt(M_PI);
}

double Phi(double mean, double sigma, double x){
    return 0.5 * (1 + erf((x - mean)/(sigma * sqrt(2))));
}


int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */   
    double mean = 205;
    double sigma = 15;
    int n = 49;
    double mean2 = n * mean;
    double sigma2 = sqrt(n) * sigma;
    double x = 9800;
    printf("%.4f", Phi(mean2, sigma2, x));
    return 0;
}

Problem solution in C programming.

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int main() {

  double weight,count,meanv,stdv;

  scanf("%lf",&weight);
  scanf("%lf",&count);
  scanf("%lf",&meanv);
  scanf("%lf",&stdv);
  

  printf("%6.4lf\n",0.5*(1.0+erf((weight-(count*meanv))/(sqrt(count)*stdv*sqrt((double)2.0)))));
  
  return 0;
}

Problem solution in JavaScript programming.

const print = o => console.log(o.toFixed(4));

function processData(input) {
    const [maxWeight, numBoxes, meanWeightBox, sdWeightBox] = input.split`\n`.map(Number);
    
    console.error(maxWeight, numBoxes, meanWeightBox, sdWeightBox);
        
    const z = ((maxWeight/numBoxes) - meanWeightBox) / (sdWeightBox / Math.sqrt(numBoxes))
    print(0.5 - 0.49010)
    
} 

process.stdin.resume();
process.stdin.setEncoding("ascii");
_input = "";
process.stdin.on("data", function (input) {
    _input += input;
});

process.stdin.on("end", function () {
   processData(_input);
});