Revision as of 01:53, 27 June 2024 by Admin (Created page with "'''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 * 250...")
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.