Day 5: Normal Distribution II | 10 Days Of Statistics | HackerRank Solution

Hello coders, today we are going to solve Day 5: Normal Distribution II HackerRank Solution which is a Part of 10 Days of Statistics Series.

Objective

In this challenge, we go further with normal distributions.

Task

The final grades for a Physics exam taken by a large group of students have a mean of U = 70 and a standard deviation of O = 10. If we can approximate the distribution of these grades by a normal distribution, what percentage of the students:

1. Scored higher than 80 (i.e., have a grade > 80)?
2. Passed the test (i.e., have a grade => 60)?
3. Failed the test (i.e., have a grade < 60)?

Find and print the answer to each question on a new line, rounded to a scale of 2 decimal places.

Input Format

There are 3 lines of input (shown below):

70 10
80
60

The first line contains 2 space-separated values denoting the respective mean and standard deviation for the exam. The second line contains the number associated with question 1. The third line contains the pass/fail threshold number associated with questions 2 and 3.

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

Output Format

There are three lines of output. Your answers must be rounded to a scale of 2 decimal places (i.e., 1.23 format):

1. On the first line, print the answer to question 1 (i.e., the percentage of students having grade > 80).
2. On the second line, print the answer to question 2 (i.e., the percentage of students having grade => 60).
3. On the third line, print the answer to question 3 (i.e., the percentage of students having grade < 60).

Solution – Normal Distribution II

C++

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

double normal_dist(double m, double sd, double x)
{
    
    double p = 0.5*(1 + erf((x-m)/(sd*sqrt(2.0))));
    return p*100; // for percentage
}


int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */  
    
    double m = 70, sd = 10;
    
    double p1 = double(100) - normal_dist(m, sd, 80);
    double p2 = double(100) - normal_dist(m, sd, 60);
    double p3 = normal_dist(m, sd, 60);
    
    printf("%0.2f\n%0.2f\n%0.2f", p1, p2, p3);
    
    return 0;
}

Disclaimer: The above Problem (Normal Distribution II) is generated by Hacker Rank but the Solution is Provided by CodingBroz. This tutorial is only for Educational and Learning Purpose.