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...

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.

A recent study suggested that 75% of all meals marketed specifically to babies and toddlers and sold in grocery stores had high sodium content.51 This is of deep concern because increased salt in the diet can cause hypertension, which may lead to cardiovascular disease. Suppose 30 toddler meals are randomly selected and the sodium content in each is carefully measured.

a. What is the probability that exactly 23 meals will have high sodium content?

b. What is the probability that at least 25 will have high sodium content?

c. Suppose at most 20 meals have high sodium content. What is the probability that at most 15 will have high sodium content?