Question

Data analysis of the breaking strength of a certain fabric shows that it is normally distributed with a mean of 300 lb and a variance of 9.

a. Estimate the percentage of fabric samples that will have a breaking strength no less than 294 lb.

b. Estimate the percentage of fabric samples that will have a breaking strength no less than 297 lb and no greater than 303 lb.

Answer 1

Program plan:

• To write a matlab code to find the percent of fabric having breaking strength no less than 294 lb.

• To find the percentage of fabric sample that will be having breaking strength no less than 297 lb and no greater than 303 lb.

 

Program:

%**********************************************************

%A matlab code is written to find the percent of fabric

%samples that have breaking strength no less than 294 lb

%and also to find the percent of fabric samples that will

%have breaking strength no less than 297 lb and no greater

%than 303 lb using the mean and variance of the sample.

%**********************************************************

%Declaration of mean

mu=300;

%Declaration of variance

variance=9;

%Declaration of standard deviation

sigma=sqrt(variance);

%Computes the value

z1=(294-mu)/sigma;

%Computes the value

z2=(297-mu)/sigma;

%Computes the value

z3=(303-mu)/sigma;

%To find the percent of fabric samples which have breaking strength no less

%than 294lb

p1=100*(1-erf(z1/sqrt(2)))/2;

%Displays text

disp('Sample having breaking strength no less than 294lb');

%Displays value

disp(p1);

%To find the percent of fabric samples which have breaking strength no less

%then 297lb and no greater then 303lb

p2=100*(erf(z3/sqrt(2))-erf(z2/sqrt(2)))/2;

%Display text

disp('Sample having breaking strength no less than 297lb and no greater then 303lb');

%Display value

disp(p2);

 

Output:

>> Untitled

Sample having breaking strength no less than 294lb

97.7250

 

Sample having breaking strength no less than 297lb and no greater then 303lb

68.2689

a. Sample having breaking strength no less than 294lb

97.7250

 

2. Sample having breaking strength no less than 297lb and no greater then 303lb

68.2689