Answer:
(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
