George Mason student services investigated whether our undergraduate student relationship preferences match national numbers. It is known that when asked if they are currently in a relationship for longer than one month, 35% of undergraduate students answer "Yes." A researcher took a sample of 12 GMU undergraduates and asked them the same question. a) Check if this situation fits the binomial setting. Write four complete sentences addressing each requirement. Use one sentence for each requirement. b) Assuming this situation is a binomial experiment, build the probability distribution in a single table form in StatCrunch. There are two ways to do this. You may use Data → Compute → Expression and choose the function dbinom. This method relies on you entering all the outcome values of the random variable in the first column of your data table. The other way to do this is to use the binomial calculator and calculate the probability of each of the values of the random variable from X = 0 to X - 12. You may present this table horizontally or vertically and leave the probabilities unrounded. c) Calculate the probability that at least nine in this sample are in a relationship for longer than one month using the probability distribution table you created in 3(b). Show all of your calculations and use proper probability notation. Round your answer to four decimal places. d) Verify your answer to 3(c) using the StatCrunch binomial calculator. Copy the image with values below to your document. Write a one sentence interpretation of the probability in context of the question. e) Calculate the probability that between two and six (inclusive) students in this sample are currently in a relationship for longer than one month using the StatCrunch binomial calculator graph and include this image with values in your document. Write a one sentence interpretation of the probability in context of the question. f) Calculate the mean and standard deviation of the number of students in the sample who are in a relationship for longer than one month. Show your work using the binomial mean and binomial standard deviation formulas and provide your answers in your document. Round your answers to two decimal places. (It is not necessary to use StatCrunch for this part). g) Calculate the probability that exactly seven of the 12 students in this sample are in a relationship for longer than one month using the StatCrunch binomial calculator. Copy this image with values from StatCrunch into your document. Then, once you obtain your answer, write a one sentence interpretation of the probability in context of the question. h) Imagine you repeated taking a sample of 12 students from the GMU population 10,000 times. We can simulate this in StatCrunch. First, go to Data → Simulate → Binomial. Next, enter 10.000 for Rows, 1 for Columns, 12 for n. 0.35 for p,