Which of the following is not a requirement of the binomial probability distribution? Select one: O a. the procedure has an infinite number of trials O b. the trials must be independent O c. each trial is classified as a success or failure O d. the probability of a success remains the same in all trials

Every business day, Michael's alarm goes off at 06:30. The probability he hits the snooze button is 20%. a. Give the discrete probability distribution for the event that Michael's alarm does or does not go off on a business day. What type of random variable is this? Explain. b. In 8 business days, what is the probability Michael hits the snooze button at least one time? c. In 80 business days, how many times would we expect Michael to hit the snooze button? What is the associated variance?

High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?

H3. Show proper step by step calculation