Answer:
It takes less time sending 5 letters the traditional way with a probability of 36.7%.
Step-by-step explanation:
First we must take into account that:
- The traditional method is distributed X ~ Poisson(L = 1)
- The new method is distributed X ~ Poisson(L = 5)
[tex]P(X=x)=\frac{L^{x}e^{-L}}{x!}[/tex]
Where L is the intensity in which the events happen in a time unit and x is the number of events.
To solve the problem we must calculate the probability of events (to send 5 letters) in a unit of time for both methods, so:
- For the traditional method:
[tex]P(X=5)=\frac{1^{5}e^{-1}}{1!}\\\\P(X=5) = 0.367[/tex]
- For the new method:
[tex]P(X=5)=\frac{5^{5}e^{-5}}{5!}\\\\P(X=5) = 0.175[/tex]
According to this calculations we have a higher probability of sending 5 letters with the traditional method in a unit of time, that is 36.7%. Whereas sending 5 letters with the new method is less probable in a unit of time. In other words, we have more events per unit of time with the traditional method.
