Normal Distribution and area under the curve

Hello, I am just looking to make my hw a little fancier than is needed.

The question is asking to find the % of drivers that will get a ticket, if tickets are issued 72mph and above, with a mean speed of 67.

clear;clc;

x_bar=67; %mph

x_ticket=72; %mph that will receive a ticket

s=4; %standard deviation

z1=(x_ticket-x_bar)/s;

pz=0.3944; %from table 4.3

disp('The percent of drivers exceeding 72mph is')

P=(0.5-pz)*100

rng(0,'twister')

a=4; %standard deviation

b=67; %mean value

y=a.*randn(1000,1)+b;

pd=fitdist(y,'Normal')

x=[-3:.1:3]; %+/- 15 from the mean

y=normpdf(x,0,1);

plot(x,y)

I think I am rpetty close. I just want to figure out how to get MATLAB to plot this data, and shade the ticketed region. Like the picture below.

furthermore, extra points, how can i get the area under the curve?

Thanks!

R2022a (beta)

Answer 1

[David Hill]

mu=67;
sigma=4;
x=72;
y =1 - cdf('Normal',x,mu,sigma)

[Kyle Langford]

Certainly that is a better way to solve it than what I did! but that was not my question.

My question is, how do I plot this data, and shade it, like the example picture.

[David Hill]

Likely lots of ways of doing it. I just picked the first thing that came to my mind.

mu=67;
sigma=4;
x=67-4*sigma:.1:67+4*sigma;
y =pdf('Normal',x,mu,sigma);
plot(x,y)
hold on
bar(x(x>=72),y(x>=72),'FaceColor','b','EdgeColor','b');