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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