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1. At a certain airport, 75 of the flights arrive on time. A random .pdf

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A random sample of 12 flights was taken at an airport where normally 75% of flights arrive on time. The mean number of on-time flights would be 0.75 * 12 = 9, and the variance would be 0.75 * 0.25 * 12 = 3. Using Chebyshev's Inequality, the maximum probability of 7 or fewer flights or 11 or more flights being on time is 1/9. The exact probability can be calculated using the binomial probability formula.

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1. At a certain airport, 75% of the flights arrive on time. A random sample of 12 flights was selected. (a) Find the values of mean and variance for the number of flights that are on time. (b) Use Chebyshev's Inequality (p.110) to find the maximum (upper bound) of the probability for the number of the flights on time to be either no more than 7 or at least 11. (c) Use the binomial probability formula to find the EXACT probability for the number of the flights on time to be either no more than 7 or at least 11 .

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