An Apple service center has facilities to repair 30 iPads per day. Assume that i
ID: 3128589 • Letter: A
Question
An Apple service center has facilities to repair 30 iPads per day. Assume that iPads requiring repair arrive according to a Poisson process with an average of 20 per day. If more than 30 iPads arrive, the excess is turned away to another facility. Show work
Find the probability that exactly 30 iPads arrive in one day.
Find the probability that iPads are turned away to another facility.
The manager of the service center decides to add facilities so that it can service iPads arriving during a day about 95% of the time. How many iPads must it be able to service in a day?
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 = 20
x = the number of successes = 30
Thus, the probability is
P ( 30 ) = 0.008343536 [ANSWER]
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b)
There are more than 30 ipads in that case.
Note that P(more than x) = 1 - P(at most x).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 20
x = our critical value of successes = 30
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 30 ) = 0.986525319
Thus, the probability of at least 31 successes is
P(more than 30 ) = 0.013474681 [ANSWER]
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C)
We want x so that P(at most x) = 0.95, when the mean is 20.
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 20
x = the maximum number of successes = 28
Then the cumulative probability is
P(at most 28 ) = 0.965666478
28 is the smallest value that satisfies the said condition. Hence, IT MUST SERVICE AT LEAST 28 IPADS. [ANSWER]
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