Question

For the fiscal year 2007, the IRS audited 1.77% of individual tax returns with income of...

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?

Math   Statistics-And-Probability   
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Answer #1

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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