A customer support center for a computer manufacturer receives an average of 2.2
ID: 3129681 • Letter: A
Question
A customer support center for a computer manufacturer receives an average of 2.2 phone calls every five minutes. Assume the number of calls received follows the Poisson distribution. (round all answers to four decimal places)
a. What is the probability that no calls will arrive during the next five minutes?
b. The probability that 3 or more calls will arrive during the next five minutes is
c. The probability that 3 calls will arrive during the next ten minutes is
d. The probability that no more than 2 calls will arrive during the next ten minutes is
Explanation / Answer
a)
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 2.2
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.110803158 [ANSWER]
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b)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 2.2
x = our critical value of successes = 3
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 2 ) = 0.62271375
Thus, the probability of at least 3 successes is
P(at least 3 ) = 0.37728625 [ANSWER]
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c)
The new mean is not 2.2*(10min/5min) = 4.4.
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 4.4
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.174305487 [ANSWER]
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d)
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 4.4
x = the maximum number of successes = 2
Then the cumulative probability is
P(at most 2 ) = 0.185142286 [ANSWER]
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