SOLUTION: A business firm has a 24-hour toll-free telephone hotline. Calls arrive at the rate of three per hour. (Enter your answers as fractions in simplest form or as decimals rounded t

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Question 1100387: A business firm has a 24-hour toll-free telephone hotline. Calls arrive at the rate of three per hour.
(Enter your answers as fractions in simplest form or as decimals rounded to four decimal places.)
a. What is the average number of calls received on a certain 7-hour interval?
b. What is the probability that at most five calls will be received on a certain 4-hour interval?
Answer by Boreal(15235) About Me  (Show Source):
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Average number of calls will be 21, the 3 per hour * 7 hours
In 4 hours, expect 12 calls.
Poisson has parameter 12
e^(-12)*12^5/5!=0.0127
e^(-12)*12^4/4!=0.0053
e^(-12)*12^3/6=0.0018
e^(-12)*144/2=0.0004
e^(-12)*12=0.00007
rounding the last the sum is 0.0203.