Championship Billiards, owned by D & R Industries, in Lincolnwood, Illinois, provides some of the finest billiard fabrics, cushion rubber, and component parts in the industry. It sells billiard cloth in bolts and half-bolts.

A half-bolt of billiard cloth has an average length of 35 yards with widths of either 62 or 66 inches. The file titled Half Bolts contains the lengths of 120 randomly selected half-bolts.

a. Produce a relative frequency histogram for these data. Does it seem plausible the data came from a population that has a uniform distribution?

b. Provide the density, f (x), for this uniform distribution.

c. A billiard retailer, Sticks & Stones Billiard Supply, is going to recover the pool tables in the local college pool hall, which has eight tables. It takes approximately 3.8 yards per table. If Championship ships a randomly chosen half-bolt, determine the probability that it will contain enough cloth to recover the eight tables.