Answer:
a) There is a 16.0623% probability that 5 messages are received in 1 hour.
b) There is a 11.5880% probability that 10 messages are received in 1.5 hours.
c) There is a 22.4042% probability that 2 messages are received in 0.5 hours.
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
is the Euler number
is the mean in the given time interval.
In this problem, we have a mean of 6 messages per hour.
(a) What is the probability that 5 messages are received in 1 hour?
Find the value of P when and
So
There is a 16.0623% probability that 5 messages are received in 1 hour.
(b) What is the probability that 10 messages are received in 1.5 hours?
The mean is 6 messages in one hour.
For 1.5 hours, the mean is 6*1.5 = 9 messages.
So
We have to find the value of P when and .
There is a 11.5880% probability that 10 messages are received in 1.5 hours.
(c) What is the probability that less than 2 messages are received in 1/2 hour?
The mean is 6 messages in one hour.
For 0.5 hours, the mean is 6*0.5 = 3 messages.
So
We have to find the value of P when and .
There is a 22.4042% probability that 2 messages are received in 0.5 hours.