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