# Suppose the emergency room at Mass General opens at 6am and has a mean arrival rate throughout...

## Question:

Suppose the emergency room at Mass General opens at 6am and has a mean arrival rate throughout the day of 6.9 patients per hour (that is {eq}\lambda {/eq} = 6.9).

(a) What is the probability that the first patient arrives between 6am and 7am?

(b) What is the probability that the first patient arrives between 6:15am and 6:45am?

## Probability Under Poisson Distribution:

Named after French mathematician Simeon Poisson, Poisson distribution is a type of discrete probability distribution that gives probability of random and independent event(s) occurring over a given time interval or space. The average number of events occurring within a stated interval is known but exact timing is unknown. Poisson probability is also modeled in other fields such as area, distance and volume.

#### a).

The Poisson probability mass function is given by the formula below:

{eq}\displaystyle P(X=x)=e^{-\lambda}\frac{\lambda^x}{x!}\\\text{This is...

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