Question

A tax auditor is selecting a sample of 7 tax returns for an audit. If 4...

A tax auditor is selecting a sample of 7 tax returns for an audit. If 4 or more of these returns are​"improper," the entire population of 45 tax returns will be audited. Complete parts​ (a) through​ (e) below.

Q. What is the probability that the entire population will be audited if the true number of improper returns in the population is:

a) 15

b) 20

c) 5

d) 10

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Ans

a)

P(improper returns) = 15/45 = 0.33

Binomial distribution (n-7, p-0.33) f(x) Fx) 1 F) 01 0.0606 0.0606 0.9394 0.2090 0.26960.7304 2 0.3088 0.57830.4217 3 0.2535 0.8318 0.1682 0.9566 0.0434 0.99350.0065 0.0004 7 0.00041.00000.0000 4 0.1248 0.0369 5 6 0.0061 0.9996

P = 0.1682

b)

P(improper returns) = 20/45 = 0.44

P= 0.3706

c)

P(improper returns) = 5/45 = 0.11

P = 0.0039

d)

P(improper returns) = 10/45 = 0.22

P = 0.0461

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