Question

6. When you buy lumber from Home Depot, they often claim that a piece of wood is a certain length, although there is some variation because of the imprecision of tools used to cut the wood to length. Suppose that a certain type of beam has and average length of 3 feet with a standard deviation of 0.1 feet. Your plan is to connect 20 of these beams in a straight line to form a "superbeam". What is the expect length and the standard deviation of the superbeam (in feet) assuming the beams are independent from one another?

Answer 1

Let X be the length of the beam. Let the mean length of beam be E (X) = 3 feet. Let the standard deviation of the length of the beam be SD (X)=0.1. So, variance is V(x)=(0.1) = 0.01 The number of beams is 20. (beams are independent) Now, it is required to connect 20 of these beams in a straight line to form a "super beam." Let Y be the length of the super beam. So, Y=X+X+-+X(20times) = 20X The expected value of the super beam is, u= E(Y) = E(20x) = 20E(X) = 20(3) = 60 The variance of the super beam is, o? =V(Y) =V (20x) = (20 V (X) = 400(0.01) = 4 The standard deviation of super beam is, orvo? = 2