Problem 3 A. E. Write a scenario that is relevant to you and that would follow a binomial distribution with n = 20 and p = 0.25. Use a binomial calculator to find the following probabilities for your scenario. A. Probability of exactly 4 successes. B. Probability of at least 4 successes. . What the expected number of successes? What is the standard deviation? Show your work. How many successes would be unusually high? Give your answer as a whole number. Show how you calculated your answer. Interpret your answer for part D in a sentence using the context of the scenario that you wrote. Problem 4 Suppose the scores on an exam are normally distributed with a u = 72 points, and o = 5 points. Answer the following questions. A. B. A student is randomly selected. What is the probability that the student scored between 76 and 80 points? Sketch a graph of the probability. Write your answer as a decimal rounded to four decimal places. The instructor wanted to "pass" anyone who scored above 68. What percentage of exams will have passing scores? Sketch a graph have passing scores? Sketch a graph representing your answer. Round to the nearest whole percent. Suppose that the top 5% of the exams will be given an A+. In order to be given an A+, an exam must earn at least what score? Sketch a graph representing your answer. Round to the nearest whole number. What is the probability of getting an exam score that is more than 1.4 standard deviations above the mean (i.e. the probability of getting a z-soore greater than 1.4)? . What is the exam score for an exam whose z- soore is 1.4