In a rough approximation of a baseball game assume the game ends after each team gets...

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In a rough approximation of a baseball game assume the game ends after each team gets 27 outs. So far during the 2022 MLB season, the median number of strikeouts during a game for a team is roughly 9. Let X be the random variable representing the number of strikeouts a team gets per game. Let's model the number of strikeouts per game, X, using the Binomial distribution. a) Calculate the probability, , of an out being a strikeout, and calculate the standard deviation for the number strikeouts per game. b) Using the Binomial distribution and the probability estimate of you computed in part (a), create a plot of the probability of each number of strikeouts per game from 0 to 27. c) What is the P(X ≤ 8), the probability that a team has less than or equal to 8 strikeouts in a game? d) What is the P(X ≥ 12), the probability of having 12 or more strikeouts in a game? e) What is the probability of having the median number, 9, strikeouts in a game? f) Given your values of n and x, compute the typical strikeout streak length within a game? Comment on your findings in the context of a baseball game (note your textbook defines typical streak as: In(n(1-))). In a rough approximation of a baseball game assume the game ends after each team gets 27 outs. So far during the 2022 MLB season, the median number of strikeouts during a game for a team is roughly 9. Let X be the random variable representing the number of strikeouts a team gets per game. Let's model the number of strikeouts per game, X, using the Binomial distribution. a) Calculate the probability, , of an out being a strikeout, and calculate the standard deviation for the number strikeouts per game. b) Using the Binomial distribution and the probability estimate of you computed in part (a), create a plot of the probability of each number of strikeouts per game from 0 to 27. c) What is the P(X ≤ 8), the probability that a team has less than or equal to 8 strikeouts in a game? d) What is the P(X ≥ 12), the probability of having 12 or more strikeouts in a game? e) What is the probability of having the median number, 9, strikeouts in a game? f) Given your values of n and x, compute the typical strikeout streak length within a game? Comment on your findings in the context of a baseball game (note your textbook defines typical streak as: In(n(1-))).

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a To calculate the probability of an out being a strikeout we divide the median number of strikeouts ... View the full answer