During the national sports day held at Kuala Lumpur, a number of athletes tested positive for the hidden presence of banned supplements and lost the opportunity to compete in the games. There was about 1% reported violations of anti-doping rules from the entire population of athletes. You have been asked to study this further. For this purpose you select a random sample of 2,000 athletes who are representative of the population and you find that 26 athletes have used the banned supplements during the past 6 months.

a. What is the probability the banned supplements were used during the past 6 months in less than your sampled proportion?

b. Determine the probability for part a if 0.8% of the athletes from the sample were reported to have used the banned supplements during the past 6 months.

Comment on the differences between the findings in parts a and b.

c. Determine the probability that the proportion between 0.5% and 1.5% of the athletes is using the banned supplements during the past 6 months.