WEEK 6: MATH 110 HOMEWORK on Canvas Exam 2 3. The Columbian Coffee Company claims that 56% of the general public enjoys a cup of coffee. Mia surveys her ten friends to see if they would enjoy a cup of coffee at this weekend's gathering. a. Why is this a binomial distribution? b. What constitutes a success on a single trial? c. What is the probability of success on a single trial? d. What are the possible values of the random variable? e. Find the probability that all ten friends would enjoy a cup of coffee. State the formula or screen. f. Find the probability that at most nine friends would enjoy a cup of coffee. g. Find the probability that one or none would enjoy a cup of coffee? 4. Several statistics students are unprepared for a multiple-choice exam with 40 questions, and all of their answers are guesses. Each question has five possible answers, and only one of them is correct. a. State the probability of success. Use the correct symbol. b. What are the possible values of the random variable? c. Find the mean for the number of correct answers for such students. d. Find the standard deviation for the number of correct answers for such students. e. Would it be significantly high for a student to pass by guessing and getting at least 28 correct answers? Why or why not? f. Find the probability of between 8 and 10 correct answers, inclusive. g. Find the probability of between 8 and 10 correct answers, exclusive.