A Normal Distribution restart; Normal Probability Density Function We wish to find the graph of the normal probability density function with mean NiMvJSNtdUciJCsi and standard deviation NiMvJSZzaWdtYUciIzU=. The formula for this function is NiMvLSUiZkc2IyUieEcqJiIiIkYpKiYiIzVGKS0lJXNxcnRHNiMqJiIiI0YpJSNQaUdGKUYpISIi NiMtJSRleHBHNiMsJComKSwmJSJ4RyIiIiIkKyIhIiIiIiNGKyIkKyNGLUYt . We enter the formula easily the Maple way.. f:=(1/(10*sqrt(2*Pi)))*exp(-(x-100)^2/200); Now we plot the graph. plot(f,x=50..150); The graph looks like it is 0 to the left of 60 and to the right of 140. But let's check f(200). evalf(subs(x=200,f)); Pretty small, but still there. Now let's check f(20000). evalf(subs(x=20000,f)); Also still there. Actually, f(NiMlInhH) > 0 for all NiMlInhH. Now let's find the integral from negative to positive infinity. int(f,x=-infinity..infinity); Next we want to find the second derivative of the function. f2:=diff(f,x\$2); To find the NiMlInhH-values of the inflection points, we set the second derivative equal to 0 and solve for NiMlInhH. solve(f2=0,x); Notice that these two NiMlInhH-values of the points of inflection are exactly one standard deviation from the mean in each direction. Now let's take the integral covering one standard deviation in each direction. evalf(int(f,x=90..110)); Covering two standard deviations. evalf(int(f,x=80..120)); Covering three standard deviations. evalf(int(f,x=70..130)); Normal Probability Distribution (Cumulative Density) Function Now we wish to find the graph of the normal probability distribution (cumulative density) function with mean NiMvJSNtdUciJCsi and standard deviation NiMvJSZzaWdtYUciIzU=. The formula for this function is NiMvLSUiRkc2IyUieEctJSRpbnRHNiQqKCIiIkYsKiYiIzVGLC0lJXNxcnRHNiMqJiIiI0YsJSNQaUdGLEYsISIiLSUkZXhwRzYjKiYpLCQsJiUieUdGLCIkKyJGNUY1RjNGLCIkKyNGNUYsL0Y9OywkJSlpbmZpbml0eUdGNUYn. We enter the formula. restart; f:=(1/(10*sqrt(2*Pi)))*exp(-(y-100)^2/200); F:= int(f,y=-infinity..x); plot(F,x=50..150); Let's check some values. "F(-infinity)"=evalf(subs(x=-infinity,F)); "F(50)"=evalf(subs(x=50,F)); "F(100)"=evalf(subs(x=100,F)); "F(150)"=evalf(subs(x=150,F)); "F(infinity)"=evalf(subs(x=infinity,F));