Exercise


ABy Admin
Jun 27'24

Answer

Solution: A

By the central limit theorem, the number of passengers for either train is approximately normally distributed with mean 1000*1/2 = 500 and variance 1000 * 1/2 *1/2 = 250. Therefore the minimum number of seats needed equals the 99th percentile of a normal distribution with mean 500 and variance 250. The 99th percentile of a standard normal is 2.326 which implies that the 99th percentile for the number of passengers for each train is

500 + 2.326 * 2501/2 =  536.78

Hence the answer is 537.

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