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A children's hospital has reported that an average of 6 patients arrive in the emergency room...

A children's hospital has reported that an average of 6 patients arrive in the emergency room each hour. Arrivals at this emergency room are known to follow a Poisson probability distribution.

a.) What is the probability that exactly 10 patients will arrive in the emergency room between 1:00 pm and 2:00 pm today?

b.) What is the probability that no more than 3 patients will arrive in the emergency room between 6:30 pm and 7:30 pm today?

c.) What is the probability that exactly 1 patient will arrive in the emergency room between 11:00 am and 11:30 am today?

d.) If 6 patients arrive in the emergency room each hour, what is the variance of this probability distribution?

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