SOLUTION: Jack and Jill work in the school office. They are recording and analysing the number and length of phone calls received. The number of telephone calls that are answered by the offi

Question 1086754: Jack and Jill work in the school office. They are recording and analysing the number and length of phone calls received. The number of telephone calls that are answered by the office has a mean of 12 calls per hour.
a) Find the probability that there are no calls in any given 15 minute interval.
I need to use distribtuions on a scientific caclulator but I don't know which to use, I tried poisson and binomial but it didn't work.
Your help is much appreciated, thankyou

Found 2 solutions by Boreal, mathmate:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Poisson distribution with calls proportional to the time. Expect 3 calls in 15 minutes, so lambda is 3.
Probability x=0 when lambda is 3:
formula is e^(-x)*lambda^x/x!
0!=1
e^(-3)*3^0/0!
=e^(-3)=0.0498.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
Jack and Jill work in the school office. They are recording and analysing the number and length of phone calls received. The number of telephone calls that are answered by the office has a mean of 12 calls per hour.
a) Find the probability that there are no calls in any given 15 minute interval.
I need to use distribtuions on a scientific caclulator but I don't know which to use, I tried poisson and binomial but it didn't work.

Solution:
Wonder if you did the same as following when you worked on the Poission distribution.
For a 15 minute period, the average number of calls is λ=12/4=3
P(k=0 calls within period)
=Pmf_Poisson(0,3)
=λ^k (e^(-λ)/k!
=3^0 (e^(-3)/0!
=1*e^(-3)/1
=e^(-3)
=0.0498

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