Penalty Kicks. In the game of soccer, a penalty kick is a direct free kick, taken from 12 yards out from the goal on the penalty mark. According to the article “Penalty Kicks in Soccer: An Empirical Analysis of Shooting Strategies and Goalkeeper’s Preferences” (Soccer&Society, Vol. 10, No. 2, pp. 183–191) by M. Bar-Eli and O. Azar, 85% of penalty kicks placed by professional soccer players are successful. In 15 penalty kicks by professional soccer players, what is the probability that a. all are successful? b. at least 13 are successful? c. Find and interpret the mean and standard deviation of the number of successful penalty kicks out of 15.

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