The number of people arriving for treatment at an emergency room can be modeled by apoisson process with a rate parameter of 5/hr.(a) what is the probability thatexactly fourarrivals occur during a particular hour? (b) what is the probability thatat least threepeople arrive during a particular hour? (c) how many people do you expect to arrive during a45-minuteperiod?

(a) The probability of having exactly four arrivals during a particular hour is 0.1754.

(b) The probability that at least 3 people arriving during a particular hour is 0.7350.

(c) The expected arrivals in a 45 minute period (0.75 hours) is 3.75 arrivals.

Step-by-step explanation:

(a) If the arrivals can be modeled by a Poisson process, with λ = 5/hr, the probability of having exactly four arrivals during a particular hour is:

The probability of having exactly four arrivals during a particular hour is 0.1754.

(b) The probability that at least 3 people arriving during a particular hour can be written as

Using

We get

The probability that at least 3 people arriving during a particular hour is 0.7350.

(c) The expected arrivals in a 45 minute period (0.75 hours) is