day6_1

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

//Credit for erf: https://introcs.cs.princeton.edu/java/21function/ErrorFunction.java.html
float errorFunction(float z) {

        double t = 1.0 / (1.0 + 0.5 * abs(z));

        // use Horner's method
        double ans = 1 - t * 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;
}

float normal(float x, float stdDev, float mean){
    float Z = (x-mean) / stdDev;
    return 0.5*(1 + (errorFunction((Z/(sqrt(2))))));
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */  
    const int maxWeight = 9800; 
    const int n = 49;
    const int mean = 205;
    const int stdDev = 15;
    // When n > 30 we can use central limit theorem.
    // For large n, the distribution of sample sums is close to normal distribution  where meanPrime = n * mean, and sigmaPrime = sqrt(n) * sigma: 
    float meanPrime = n * mean;
    float sigmaPrime = sqrt(n) * stdDev;
    // Print the probability that the eleveator can successfully transport all 49 boxes. 
    
    float probability = normal(maxWeight, sigmaPrime, meanPrime);
    cout << fixed << setprecision(4) << probability;
    return 0;
}