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5.2.q7 - Student Grady Simonton Course Math119 Elementary...

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Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 492.39 Instructor: Shawn Parvini - 16 weeks Date: 3/18/10 Book: Triola: Elementary Statistics, 11e Time: 4:23 PM There is a 0.0084 probability that a best-of—seven contest will last four games, a 0.1584 probability that it will last five games, a 0.2891 probability that it will last six games, and a 0.5441 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation. Is it unusual for a team to "sweep" by winning in four games? For the data to be a probability distribution, the individual probabilities must sum to 1 and none of the values can be greater than 1 or less than 0. Find the sum of the probabilities. 2130‘) = Xfour + xfive + xsix + xseven 0.0084 + 0.1584 + 0.2891 + 0.5441 1 Also note that all the individual probabilities are less than or equal to l and greater than or equal to zero. Since both conditions are met, this data is a probability distribution. Now, find the mean of the probability distribution using the formula below. u = Z [x - P(x)] = xfour ‘ P(xfour) +xfive ' Poi five) +xsix ‘ P(xsix) + xseven ‘ P(xseven) = 4 - 0.0084+ 5 - 0.1584+ 6 - 0.2891 +7 - 0.5441 = 6.3? Find the standard deviation of the probability distribution using the formula below. 5 = lZW-Pon—uz = ii x gout ‘ 130‘ four) + xgive ‘ 130‘ five) + xgin ‘ P(xsix) + xgeven ‘ P(X seven) _ 1'12 = V42 - 0.oos4+ 52 - 0.1534+ 62 - 0.2391+ 72 - 0.5441 — 6.372 = 0.77 An event is considered unusual if the probability of it occurring is less than or equal to 0.05. Page 1 ...
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