#include <bits/stdc++.h>
#include <math.h>

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 mu = 205 pounds and a standard
// deviation of sigma = 15 pounds. Based on this information, what is
// the probability that all 49 boxes can be safely loaded into the
// freight elevator and transported?

// The central limit theorem (CLT) states that, for a large enough
// sample (n), the distribution of the sample mean will approach normal
// distribution. This holds for a sample of independent random
// variables from any distribution with a finite standard deviation.

// mu' (mean) = n * mu
// sigma' (stddev) = sqrt(n) * sigma

int main()
{
    int n = 49 /* boxes */;
    int mean = n * 205 /* lbs */;         // mu
    int stddev = sqrt(n) * 15 /* lbs */;  // sigma

    // Probability P(X <= x)
    auto normalCDF = [](double x, double mean, double stddev)
    {
        double val = (x - mean)/(stddev * sqrt(2));
        return 0.5 * (1 + (erf(val)));
    };
    
    double answer_1 = normalCDF(9800 /* lbs */, mean, stddev);

    cout << fixed << setprecision(4) << answer_1 << endl;
}