Stats - Central Limit Theorem - Normal Distribution with multiple items, C++ (gcc)

Stats - Central Limit Theorem - Normal Distribution with multiple items

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

//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 boxes can be safely loaded into the freight elevator and transported?
double normalised_standard_distribution( double mean, double sd, double x){
    double ans = 0.5 * ( 1 + erf( (x - mean)/ (sd * sqrt(2))) ); //note could use pow(2.0,0.5) as sqrt(2)
    return ans;
}

// For larger sample sizes use central limit theorem
double central_limit_theorm(double mean, double sd, double x, double num){
    return normalised_standard_distribution( num*mean, sqrt(num)*sd, x );
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */
    double x, num, mean, sd;
    cin >> x >> num >> mean >> sd;
    
    // as a larger sample size, use central limit theorem on top of standard distribution
    double ans = central_limit_theorm(mean, sd, x, num);
        
    cout << fixed << setprecision(4);
    cout << ans << endl;
    return 0;
}
// Also works for
//The number of tickets purchased by each student for the University X vs. University Y football game follows a distribution that has a mean of  and a standard deviation of .
//250,100,2.4,2.0
//A few hours before the game starts,  eager students line up to purchase last-minute tickets. If there are only tickets left, what is the probability that all  students will be able to purchase tickets?


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