7.39 To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.25 inch and standard deviation 0.006 inch and that the diameter of a randomly selected hole is a random variable with mean 0.253 inch and standard deviation 0.002 inch. Let x1 5 peg diameter, and let x2 5 denote hole diameter.

a. Why would the random variable y, defined as y 5 x2 2 x1, be of interest to the furniture manufacturer?

b. What is the mean value of the random variable y?

c. Assuming that x1 and x2 are independent, what is the standard deviation of y?

d. Is it reasonable to think that x1 and x2 are independent?

Explain.

e. Based on your answers to Parts

(b) and (c), do you think that finding a peg that is too big to fit in the predrilled hole would be a relatively common or a relatively rare occurrence? Explain.