Rectangular plates are manufactured whose lengths are distributed N(2.0, 0.12) and whose widths are distributed N(3.0 0.22). Assume the lengths and widths are independent. The area of a plate is given by A= XY.

a. Use a simulated sample of size 1000 to estimate the mean and variance of A.

b. Estimate the probability that P(5.9

c. Construct a normal probability plot for the areas. Is the area of a plate approximately normally distributed?

Step 1 of 4:

The length of manufactured rectangular plates are distributed N(2.0,0.12), and whose width are distributed N(3.0,0.22). The lengths and widths are independent. The area of the plate is given by

A= XY.

Step 2 of 4:

We have to estimate the mean and variance of A by using a simulated of sample size 1000.Let X denote the length of the rectangular plate, and Y denote the width of the rectangular plate.

It is given that X~N(2.0,0.1), and Y~N(3.0,). We can simulate a sample of 1000 by using minitab software as:

Calc- Random data- distribution- parameters(with sample size) - ok (store the data in column 1 and column 2 respectively).

Since it is given that X and Y are independent

E(XY) =E(X) E(Y)

= 2 3

= 6

The simulation results will be approximate. That will change according to the sample.We can find the mean and variance of XY by using minitab as:

Find the column XY

Stat- Basic statistics - Display descriptive statistics- select the variable(XY)- statistics-ok.

(exactly), ,

Therefore the estimate of mean and variance of the area of rectangle A are and .