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Suppose X, Y, and C represent the length, width, and perimeter of a flat rectangular sheet...

Suppose X, Y, and C represent the length, width, and perimeter of a flat rectangular sheet metal part. Note that X is a normal random variable having a mean of 15 cm and a standard deviation of 1 cm, and Y is independent of X and normally distributed with a mean of 25 cm and a standard deviation of 2 cm. Determine the following. Determine Pr(C>83).

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Answer #1

Ans:

Perimeter=2X+2Y

Distribution for C:

mean=2*15+2*25=30+50=80

standard deviation=sqrt(2^2*1^2+2^2*2^2)=4.472

C is normally distributed with mean=80 and standard deviation=4.472

z=(83-80)/4.472

z=0.671

P(C>83)=P(z>0.671)=0.2512

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