Question

In: Statistics and Probability

The IRS reports that 15% of returns where the adjusted gross income is more than $1,000,000 will be subject

The IRS reports that 15% of returns where the adjusted gross income is more than $1,000,000 will be subject to a computer audit. For the year 2017, Fred Friendly, CPA, completed 16 returns where the adjusted gross income was more than $1,000,000.
a. What is the probability exactly one of these returns will be audited?
b. What is the probability at least one will be audited?

Solutions

Expert Solution

The available information shown in below table,

Sample Size Percentage
n = 16 p = 15% = 0.15

 

a)

Calculate the probability that exactly one of these returns will be audited.

             = 16 × 0.15 × 0.0874

             = 0.2097

 

Hence, the required probability is, 0.2097.

 

b)

Calculate the probability that at least one will be audited.

P(X ≥ 1) = 1 – P(X < 1)

              = 1 – P(X = 0)

= 1 – (1 × 1 × 0.0743)

= 1 – 0.0743

= 0.9257

 

Hence, the required probability is, 0.9257.

 

 

Junaid answered 2 years ago
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