A Normal Distributionrestart;Normal Probability Density FunctionWe wish to find the graph of the normal probability density function with mean NiMvJSNtdUciJCsi and standard deviation NiMvJSZzaWdtYUciIzU=. The formula for this function is NiMvLSUiZkc2IyUieEcqJiIiIkYpKiYiIzVGKS0lJXNxcnRHNiMqJiIiI0YpJSNQaUdGKUYpISIiNiMtJSRleHBHNiMsJComKSwmJSJ4RyIiIiIkKyIhIiIiIiNGKyIkKyNGLUYt . 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) FunctionNow 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));