Students enter the bathroom according to a Poisson process at a rate of 7.5 arrivals per...

Students enter the bathroom according to a Poisson process at a rate of 7.5 arrivals per minute.

What is the probability that exactly 46 students enter between 3:00 and 3:05?
Given that 6 students enter the bathroom between 4:00 and 4:01, what is the probability that exactly 36 students enter between 4:00 and 4:07?
Each student entering the bathroom has a .15 probability of wearing a hoodie, independent of other students. What is the probability that exactly 10 students wearing a hoodie enter the bathroom between 4: and 4:07?

Expert Solution

orchestra answered 1 year ago

Assume that the Poisson process X = {X(t) : t ≥ 0} describes students’ arrivals at...

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