For the fiscal year 2007, the IRS audited 1.77% of individual
tax returns with income of $100,000 or more. a. Would it be unusual
for a return with income of $100,000 to be audited?
b. What is the probability that two randomly selected returns with
income of $100,000 will be audited?
c. What is the probability that two randomly selected returns with
income of $100,000 will not be audited?
d. What is the probability that at least one of two randomly
selected returns with income of $100,000 will not be audited?
a) A value is considered unusual if the probability is less than 0.05
P(a return with income of $100,000 to be audited), p = 0.0177
Therefore, it would be unusual for a return with income of $100,000 to be audited.
b) P(two randomly selected returns with income of $100,000 will be audited) = 0.01772
= 0.0003
c) P(two randomly selected returns with income of $100,000 will not be audited) = (1-0.0177)2
= 0.9649
d) P(at least one of two randomly selected returns with income of $100,000 will not be audited) = 1 - P(two randomly selected returns with income of $100,000 will be audited)
= 1 - 0.0003
= 0.9997
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