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12) Given {2, 3, 4, 5, 6, 7, 8, 9, 10, 11} , draw 4. a) Find P (3 are even drawing with replacement) b) Find P (2 are odd drawing without replacement) BONUS Compare the sum of three 6-sided dice with the sum of two 9-sided dice = {1, 2, 3,...,9} + {1, 2, 3,...,9} Discuss range, M , O , width, and anything else you observe!, Inc. claime .. 10) How many standard deviations wide is: a) Our triangular distribution? b) The distribution in problem #7? c) The probability distribution for the sum of 72 dice?*) I have 9 colored 6-sided dice. The colors are 2 blue, 3 red, 1 green, 1 purple, and 2 yellow. I draw one from a hat and roll it, then the second, etc. until all are rolled. How many different outcomes would be possible? Do not sum! Order of colors and numbers matters:UP 3) Mars, Inc. claims that 20% of its M&M plain candies are orange: for a bag of n=100 M&Ms: a) Find the mean & std. deviation for the number of orange candies. b) If a bag has 27 M&Ms that are orange, is this unusual? c) What is the p-value for 28 orange? d) Find the highest orange count that is unusually low. e) What is the probability of getting between 16 and 25 orange M&Ms? 9) Find the Normal Probability for rolling a total between 17 & 26 inclusive, with six dice. Also, find the actual probability from your histogram, and compare the two numbers