Medicine and Clinical Studies A recent study suggests that total knee joint replacement surgery may be related to weight gain. Researchers who studied records from the Mayo Clinic Health system report that 30% of these patients gained 5% or more of their body weight following surgery.50 Suppose this percentage is the same at all hospitals in the United States and 40 people who had total knee joint replacement surgery are selected at random.
a. What is the probability that exactly 14 will experience a weight gain?
b. Find the largest value w such that the probability of w or fewer patients who experience a weight gain is at most 0.20.
c. Suppose 16 patients experience a weight gain. Is there any evidence to suggest that the proportion of patients with knee joint replacement surgery who experience a weight gain has changed? Justify your answer.