Please show matlab code thank you Develop your own ztable by

Please show matlab code, thank you.

Develop your own z-table by numerically integrating the probability density function for the standard normal distribution. Compare with MATLAB\'s built-in normedf. (Relevant MATLAB function: trapz, cumtrapz)

Solution

//below code can be used to find standard normal cumulative distribution using trapz

clear all, close all, clc, format compact, format long g;

%% Numerical integration of a function from x1 to x2

F = @(t)(sin(t)); % function to integrate

x1=0; x2=pi; % limits

a1 = quad(F,x1,x2); % use quad to integrate

%% Show the curve and display a message to define the problem

fplot(F,[x1,x2]) % a quick way to plot a function

msg = sprintf(\'What is the integral of %s from %.2f to %.2f?\',func2str(F),x1,x2);

disp(msg); waitfor(msgbox(msg));

%% Show the result

msg = [\'Area calculated by the quad function = \' num2str(a1,10)];

disp(msg); waitfor(msgbox(msg));

%% Approximate the integral via trapz for different numbers of points

for np=[5 10 25 50]

clf % clear the current figure

hold on % allow stuff to be added to this plot

x = linspace(x1,x2,np); % generate x values

y = F(x); % generate y values

a2 = trapz(x,y); % use trapz to integrate

% Generate and display the trapezoids used by trapz

for ii=1:length(x)-1

px=[x(ii) x(ii+1) x(ii+1) x(ii)];

py=[0 0 y(ii+1) y(ii)];

fill(px,py,ii)

end

fplot(F,[x1,x2]); % plot the actual curve for reference

msg = sprintf(\'Area calculated by trapz function with %u points = %.8f\',np,a2);

disp(msg); waitfor(msgbox(msg));

end