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Using Excel to compute binomial and Poisson probabilities Directions: Please type your responses directly into this document, using good document layout and format techniques, your complete responses to the prompts below. Be sure to provide responses for everything that is asked. Saiyour results in PDF format and then upload into Moodle for submission. Problem: Every year, a group of high school statistics students survey local businesses about the impact corporate recycling programs have on the city's sustainability goals. Paper surveys sent by mail, online electronic surveys, and phone surveys are each administered to a random sample of 100 local businesses. From past surveys, the students expect that 23% of the businesses will respond to the mail survey. What is the probability that 13 businesses will respond to the survey? 1) Does this problem satisi the binomial distribution criteria? Explain in detail and list your justication for or against each binomial criteria. 2) Assume that you can model this problem above using a binomial distribution. What does n = . What does p= What does x= ? 3) Calculate the following using Excel. Report the probability and the Excel feature (with arguments) that you used to obtain the answer: (a) What is the probability that exactly 41 businesses respond? (b) What is the probability that at most 24 businesses respond? (c) What is the probability that more than 60 businesses respond? 4) In what other way can the problem above be framed as a binomial probability distribution problem? Using information from the problem, and your own numerical values when needed, demonstrate how your revised perspective above on the problem ts the binomial distribution criteria and show the necessary actions in Excel that would be needed to obtain a probability result. That is, be sure to report the feature you used in Excel and the associated arguments. 5) In what other way can the problem above be framed as a Poisson probability distribution problem? Using information from the problem, and your own numerical values when needed, demonstrate how your revised perspective above on the problem fits the Poisson distribution criteria and show the necessary actions in Excel that would be needed to obtain a probability result. That is, be sure to report the feature you used in Excel and the associated arguments. Binomial 6. An instructor gives a 10 item multiple choice test. A student must answer at least 6 items correctly in order to past the test. Each item has 5 possible responses to chose from. If a student just guesses on every problem, what is the probability of a student passing the test? Assume that for each question, the response choices are equally likely. What is p = what is 11