Answer:
a) 0.045 = 4.5% probability that exactly two arrivals occur during a particular hour
b) 0.983 = 98.3% probability that at least two people arrive during a particular hour
c) 4.5 arrivals during a 45-min period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
Poisson process with a rate parameter of six per hour.
This means that . So
(a) What is the probability that exactly two arrivals occur during a particular hour?
This is P(X = 2).
0.045 = 4.5% probability that exactly two arrivals occur during a particular hour
(b) What is the probability that at least two people arrive during a particular hour?
Either less than two people arrive during a particular hour, or at least two do. The sum of the probabilities of these events is decimal 1. So
We want
In which
0.983 = 98.3% probability that at least two people arrive during a particular hour
(c) How many people do you expect to arrive during a 45-min period? people
An hour has 60 mins.
45/60 = 3/4.
So
4.5 arrivals during a 45-min period.