Manufacturing and Product Development Oriental rugs are made from various wools and woven in several different countries. The pile height (in millimeters) of an Oriental rug varies slightly and can be modeled by a uniform random variable on the interval [6, 10].

a. Carefully sketch a graph of the density function for pile height.

b. What is the probability that a randomly selected Oriental rug will have pile height less than 7 mm?

c. What is the probability that a randomly selected Oriental rug will have pile height between 8.5 and 9.5 mm?

d. Find a value h such that 90% of all Oriental rugs have pile height less than h.