Answer:
A. P(x>12 in 5 minutes)=0.0201
Step-by-step explanation:
Because we are working with a Poisson Distribution of probability, we need to get all the data needed. In a Poisson distribution is needed a constant called λ that symbolizes the mean data (6 calls) per unit of time (5 minutes), for this distribution λ=6/5.
Poisson probabilities work like this:
Remember y has to be an integer and the units of z must be the same unit of time used in λ. Now we are ready to solve this problem
A. The question is asking for the probability that in 5 minutes appear more calls than the phone-answering machine could answer (i.e P(x>12 in 5 minutes)). Because there are infinite numbers greater than 12, we are using this property of probabilities that´ll help us simplify the problem:
P(x>12 in 5 minutes)= 1 - P(x≤12 in 5 minutes)
Now we can use the following:
And you can find P(x=n in 5 minutes) for every n using a calculator or a computer, and finally add them to get
P(x≤12 in 5 minutes)= 0.9799
P(x>12 in 5 minutes)= 1-0.9799
This will be our answer
P(x>12 in 5 minutes)= 0.0201