3. (Binomial Distribution) There are 100 multiple choice questions on an exam, each having responses a, b, c, or d. Suppose each student has probability of p of correctly answering a question chosed at random from a universe of possible questions. In addition, the answers from question to question are independent. Let random variable X be the number of questions for 2 which the student answers correctly. 3 4 (a) We can see the distribution of X is Binomial distribution with n anp. What are n and p? Expression: X B(n, p); X ~ B (n = 5 6 (b) What is the probability that the student will score exactly 25 of 100 points? (If possible, use Excel function, "binom.dist") 7 (c) What is the probability that the student will score more than 25 points? (If possible, use Excel function, "binom.dist") 8 0 (d) On average, how many points the student will score? 1 2 3

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