SOLUTION: An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another and follow a Poisso

Algebra ->  Probability-and-statistics -> SOLUTION: An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another and follow a Poisso      Log On


   

Question 61689: An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another and follow a Poisson model.
a) Find the probability that the executive will receive 13 calls between 2 and 4 P.M. on a particular afternoon.
b) Find the probability that the executive will receive seven calls between 2 and 3 P.M. on a particular afternoon.
c) Find the probability that the executive will receive at least five calls between 2 and 4 P.M. on a particular afternoon.
d) Find the probability that the executive will receive three or less calls between 2 and 3 P.M. on a particular afternoon.
e) Find the probability that the executive will receive eight or more calls between 2 and 4 P.M. on a particular afternoon.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another and follow a Poisson model.
-------------
Formula:
P(X=k)=((m^k)/k!)e^(-m)
where k is the number of occurrencenses you are looking for and
m is the number expected in that time period.
In your problem m=10 in 2 hrs or 5 occurences per hour.
-----------------
a) Find the probability that the executive will receive 13 calls between 2 and 4 P.M. on a particular afternoon.
P(X=13)=(10^13)/13!)e^(-10)=0.0729...
-------------
b) Find the probability that the executive will receive seven calls between 2 and 3 P.M. on a particular afternoon.
Same formula; use k=7 and m=5
-------------
c) Find the probability that the executive will receive at least five calls between 2 and 4 P.M. on a particular afternoon.
Comment: I don't have a cumulative distribution table for Poisson, so cannot
give you a result on this or on your d or e problems.
----------------
d) Find the probability that the executive will receive three or less calls between 2 and 3 P.M. on a particular afternoon.
e) Find the probability that the executive will receive eight or more calls between 2 and 4 P.M. on a particular afternoon.
Cheers,
Stan H.