day6_3

//In this challenge, we practice solving problems based on the Central Limit Theorem.//

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

float const errorFunction(const float stdDev, const float zScore, const int population)
{
    float stdErr = stdDev/sqrt(population);
    return stdErr*zScore;
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT
       You have a sample of 100 values from a population with mean 500 and with standard deviation 80. 
       Compute the interval that covers the middle of the 95% distribution of the sample mean; in other words, compute A and B such that P(A < x < B)=0.95. 
       Use the z-value of 1.96. */

    const int mean = 500;
    const int stdDev = 80;
    const float zScore = 1.96;
    const int population = 100;

    float lowerSum = mean - errorFunction(stdDev, zScore, population);
    float higherSum = mean + errorFunction(stdDev, zScore, population);

    cout << fixed << setprecision(2) << lowerSum << endl << higherSum;
    return 0;
}