Rectangular plates are manufactured whose lengths are distributed N(2.0, 0.12) a

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. That is, generate 1000 areas for 1000 rectangular plates of length X and width Y.
B. Construct the normal probability plot of A (areas). Is there evidence to suggest that the areas are non-normal? Explain.
C. Estimate the mean and variance of A.
D. Estimate the probability that P(5.9 < A < 6.1).

Explanation / Answer

Solution:

length=N(2.0,0.12)

width=N(3.0,0.22)

A=xy

area=1000(2.0*3)+1000(0.12*0.22)

          =6.0264

b..plot attached

>>there is no evidence to say that areas are non-normal

c..variance=(6.0264-6.0000)^2/n-1

                   =0.0006967

d..probability 0.0264*(6.1-5.9=0.00528

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