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Bonus: Modeling Binomial & Geometric Distributions using M&M’s Do Not Eat Until Complete! Binomial Distributions: Suppose that the BLUE M&M is defective. As randomly as possible, select a sample of 10 M&Ms and record the number of blue ones. Replace the M&Ms and repeat 5 more times, keeping track of the number of blue M&Ms. Put your results in a table. 1) Does the observed distribution seem to follow the hypothesized binomial distribution determined by the binomial n = 10 and p = .24 (according to the company, probability of blue = .24)? 2) How do the mean and standard deviation of your sample distribution compare to np and np1 p for the theoretical distribution? Geometric Distribution: Suppose that the RED M&M is defective. As randomly as possible, draw one M&M out at a time. Continue to draw out M&Ms until you get a red one. Record X = the number of M&Ms required to draw the first red. Replace the M&Ms and repeat 5 more times, recording X. Put your results in a table. 3) Does the observed distribution seem to follow the hypothesized geometric distribution determined by the p = .13 (according to the company, probability of red = .13)? 4) How do the mean and standard deviation of the class distribution compare to the theoretical distribution? Now you can eat! Enjoy! 1 p 1 and for p p2