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6. Suppose that the probability of getting an A in a particular course is 0.08, and assume that the all student grades are independent. If you randomly sample 20 students taking the course; a) Find the expected number of students that will get an A, and the standard deviation of number of students that will get an A. (b) Find the probability that no student gets an A. c) Find the probability that at most 2 students get an A (d) Find the probability that between 2 and 4 students get an A (inclusive) (e) If (in a different course), the probability that no students out of 20 got an A was 0.2000, what was the probability that a single student got an A i.e, the probability of a success)? You may assume that all students were independent, and the probability of an A does not change for this new class of 20.
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