Question

A shipping pallet holds 10 boxes. Each box holds 300 parts of different types. The part weight is normally distributed with a mean of 1 lb and a standard deviation of 0.2 lb.

a. Compute the mean and standard deviation of the pallet weight.

b. Compute the probability that the pallet weight will exceed 3015 lb.

Answer 1

Program plan:

a. To find the mean and standard deviation of the pallet weight using matlab.

b. To compute the probability that the pallet weight will exceed 3015 lb.

 

Program:

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

%A matlab code is written to find the mean and standard

%deviation of the pallet weight in the ten boxes using

%matlab. The probability that the pallet weight will exceed

%‘3015 lb’ is found using matlab.

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

%Declaration of constant

mu=1;

%Declaration of constant

sigma=0.2;

%Computes the value

mu_pallet=10*300*mu;

%Display text

disp(\'The mean is \');

%Display value

disp(mu_pallet);

%Computes the value

sigma_pallet=sqrt(10*300*sigma^2);

%Displays text

disp(\'The standard deviation is\');

%Display value

disp(sigma_pallet)

%Computes the value

p=(1-erf((3015-mu_pallet)/(sigma_pallet*sqrt(2))))/2;

%Display text

disp(\'The probability of the pallet exceeding weight 3015lb is \')

%Displays value

disp(p);

 

Output:

>> Untitled

a.

The mean is

     3000

The standard deviation is

      10.9545

b.

The probability of the pallet exceeding weight 3015lb is

       0.0855

a.

The mean is

     3000

The standard deviation is

      10.9545

b.

The probability of the pallet exceeding weight 3015lb is

       0.0855