On a summer day, buses with Tourist arrive in the Adam village according to Pois

Question

On a summer day, buses with Tourist arrive in the Adam village according to Poisson process with average of 5 buses per hour. Each bus stay over in Adam village either 1 hrs or 2 hrs with equal probabilities.
1. what is the probability distribution of number of tourist buses in Adam village at 4:00 o'clock in the afternoon?
2. each bus brings 50, 75, or 100 tourists with probabilities 1/4, 1/2, and 1/4 respectively. Calculate a normal approximation to the probability that more than 1000 bus tourists are in Adam village at 4:00 o'clock in the afternoon. (note: the number of tourist bus is distributed as the convolution of two compound Poisson distributions)

Explanation / Answer

`1)1/4

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