Rectangular plates are manufactured whose lengths are distributed N(2.0, 0.12) and whose widths are distributed N(3.0, 0.22).

Question:

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 < A < 6.1).
c. Construct a normal probability plot for the areas. Is the area of a plate approximately normally distributed?