33. Sports and Achilles Tendon Injuries Sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendon injuries. A study in The American Journal of Sports Medicine looked at the diameter (in mm)

of the injured and healthy tendons for patients who participated in these types of sports activities.10 Suppose that the Achilles tendon diameters in the general population have a mean of 5.97 millimeters (mm)

with a standard deviation of 1.95 mm.

a. What is the probability that a randomly selected sample of 31 patients would produce an average diameter of 6.5 mm or less for the healthy tendon?

b. When the diameters of the injured tendon were measured for a sample of 31 patients, the average diameter was 9.80. If the average tendon diameter in the population of patients with injured tendons is no different than the average diameter of the healthy tendons (5.97 mm), what is the probability of observing an average diameter of 9.80 or higher?

c. What conclusions might you draw from the results of part b?