In a class of 100 students, the professor wants to determine what proportion of the students can answer a simple calculus question. The professor decides to test a random sample of 20 students. In fact 30 of the students could answer the question.   (a) What is the expected number of students sampled who answer the question correctly? (b) What is the variance of the number of correct answers if the students are sampled with replacement, i.e. one student could be tested more than once? (c) What is the variance of the number of correct answers if the 20 students sampled must be 20 different students?

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