Statistics Question (PLEASE SOLVE USING R, COPY AND PASTE THE CODE AND ANSWER FROM R )

8. (15 pts) Consider the following questions: give the distribution name, carefully define the random variables you use and find the final answer. (a) (3 pts) A professor has made 20 exams of which 8 are hard, 7 are reasonable, and 5 are easy. The exams are mixed up and the professor selects 4 of them at random to give to four sections of the course she is teaching. What is the probability that no sections receivea hard test? (b) (3 pts) Suppose a representative at a credit card customer service center receives a phone call every 5 minutes on average. Find the probability that she receives 3 phone calls in 20 minutes. (c) (3 pts) Products produced by a machine has a 3% defective rate, what is the probability that the first defective occurs in the fifth item inspected. (d) (3 pts) In a class of 100 students, 25 have hardcover and 75 students have paperback textbooks. If you randomly choose 10 students in this class, find the probability that 2 of them have hardcover texts. (e) (3 pts) Emily hits 60% of her free throws in basketball games. She had 7 free throws in last week's game. What is the probability that she made at least 5 hits? 8. (15 pts) Consider the following questions: give the distribution name, carefully define the random variables you use and find the final answer. (a) (3 pts) A professor has made 20 exams of which 8 are hard, 7 are reasonable, and 5 are easy. The exams are mixed up and the professor selects 4 of them at random to give to four sections of the course she is teaching. What is the probability that no sections receivea hard test? (b) (3 pts) Suppose a representative at a credit card customer service center receives a phone call every 5 minutes on average. Find the probability that she receives 3 phone calls in 20 minutes. (c) (3 pts) Products produced by a machine has a 3% defective rate, what is the probability that the first defective occurs in the fifth item inspected. (d) (3 pts) In a class of 100 students, 25 have hardcover and 75 students have paperback textbooks. If you randomly choose 10 students in this class, find the probability that 2 of them have hardcover texts. (e) (3 pts) Emily hits 60% of her free throws in basketball games. She had 7 free throws in last week's game. What is the probability that she made at least 5 hits