The two most popular majors in a business degree are marketing and international business, with 30% of students enrolled in marketing and 18% enrolled in international business. Suppose 20 students are selected at random.

(a) What is the probability that:

(i) at least half of them are studying a marketing major

(ii) no more than a quarter are studying an international business major

(iii) between 10 and 15 are studying a marketing major?

(b) Find the mean and variance of the number of students studying a marketing major. Find the mean and variance of the total number studying a marketing or international business major.