/* Normal Curve (15 points)

The normal curve has a lot of applications in statistics.
One application that many students are familiar with is 
"grading on a curve", where the mean scores get C's and the 
outliers get F's and A's.

The Normal probability density function is defined as follows:

                1                        (x-mu)*(x-mu)
f(x) = ---------------------- * exp( -  --------------  )
       sqrt(2*Pi*sigma*sigma)            2*sigma*sigma
       
where mu is the mean of the distribution and sigma is the standard deviation.
These are the only two parameters that are required to completely specify 
a normal curve. 

Write a Complete C program that reads three values from the keyboard
(x, mu, sigma) and outputs the value f(x) of the function for that x.

Your program must use a function to calculate f(x).

SAMPLE RUN #1:
Please enter the mean mu : 0
Please enter the standard deviation (sigma): 1
Please enter a value for x: 4
The result is = 0.00013383


SAMPLE RUN #2:
Please enter the mean mu : 2
Please enter the standard deviation (sigma): 1
Please enter a value for x: 2
The result is = 0.398942

*/ 

#include <stdio.h>
#include <stdlib.h>
#include <math.h>  // this defines M_PI

double calculate(double mu, double sigma, double x)
{
	double result;
	
	result = 1.0/sqrt(2*M_PI*sigma*sigma);
	
	result = result * exp( - ((x-mu)*(x-mu)) / (2*sigma*sigma));
	return result;
}
	
	
int main(void)
{
	double mu, sigma, x;
	
	// enter the first vector
	printf("Please enter the mean mu : ");
	scanf("%lf", &mu);
	
	printf("Please enter the standard deviation (sigma): ");
	scanf("%lf", &sigma);
	
	printf("Please enter a value for x: ");
	scanf("%lf", &x);

	printf("The result is = %g\n\n", calculate(mu, sigma, x));	
	
    system("pause");
}