2. For certain personal tax returns, the IRS will compute the amount to refund a
ID: 3125990 • Letter: 2
Question
2. For certain personal tax returns, the IRS will compute the amount to refund a tax payer. Suppose the Cincinnati office of the IRS processes an average of three returns per hour that require a refund calculation.
a. What probability distribution applies to this situation?
b. What is the probability the IRS processes exactly three returns in a particular hour that require a refund calculation?
c. What is the probability the IRS does not compute a refund on any return in an hour
d. What is the probability the IRS processes at least one return in a particular hour that requires a refund calculation?
Explanation / Answer
What probability distribution applies to this situation?
A Poisson distribution of mean 3 per hour. [ANSWER]
This is becasue the number of successes per unit time is constant, so it is a Poisson distribution.
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What is the probability the IRS processes exactly three returns in a particular hour that require a refund calculation?
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 3
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.224041808 [ANSWER]
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What is the probability the IRS does not compute a refund on any return in an hour
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 3
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.049787068 [ANSWER]
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What is the probability the IRS processes at least one return in a particular hour that requires a refund calculation?
Thus, P(at least 1) = 1 - P(0) = 0.950212932 [ANSWER]
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