Answer:
a) 0.052 = 5.2% probability that exactly three arrivals occur during a particular hour
b) 0.971 = 97.1% probability that at least three people arrive during a particular hour
c) 5.25 people are expected to arrive 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 interval.
Poisson Distribution with a rate parameter of seven per hour.
This means that
(a) What is the probability that exactly three arrivals occur during a particular hour?
This is P(X = 3).
0.052 = 5.2% probability that exactly three arrivals occur during a particular hour.
(b) What is the probability that at least three people arrive during a particular hour? (Round your answer to three decimal places.)
Either less than three people arrive, or at least three does. The sum of the probabilities of these events is 1. So
We want , which is
In which
So
0.971 = 97.1% probability that at least three people arrive during a particular hour
(c) How many people do you expect to arrive during a 45-min period?
During an hour(60 minutes), 7 people are expected to arrive. So, using proportions:
5.25 people are expected to arrive during a 45-min period