A sample of 200 students is to be taken to determine which of two brands of fruit juice (A and B) is preferred in a blind taste test. Suppose that, in the whole population of students, 60% would prefer brand A.
a. What is the probability that more than two third of the sample members prefer brand A?

b. What is the probability that between 55% and 65% of the sample members prefer brand A?

c. Suppose that a sample of only 50 students was available. Indicate how the method of calculation of probabilities would differ, compared with your solutions to parts (a) and (b)?