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1. A gas station opens at a time which is Normally distributed with the mean of 8:45 am and standard deviation of 10 minutes; similarly, its closing time is Normally distributed with the mean value at 5:12 pm and standard deviation of 15 minutes. If customers arrive as a Poisson Process with an average rate of 11.3 per hour, find the mean number of customers to be served in one such day, and the corresponding standard deviation. What is the probability that more than 90 customers will be able to get their gas there tomorrow.

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