Answer to Question #183745 in Statistics and Probability for Oscar Nsue Nsue Asangono

Question

Suppose that a large company uses an accounting information system (AIS) to manage its accounting and financial data. One important function of the AIS is to continuously audit accounting information, looking for errors or incomplete or improbable information. For example, when customers submit orders online, the AIS reviews the orders for possible mistakes. Any questionable invoices are tagged and included in a daily exceptions report. Recent data collected by the company show that the likelihood is 0.10 that an order form will be tagged. As a member of the AIS team, you have been asked by the management to determine the likelihood that(1) none of the order forms are tagged in a sample of four forms? (2) there are less than three tagged order forms in the sample of four?

Answer 1

We have given that,

Probability that an order form will be tagged = 0.10

Probability that an order form will not be tagged = 0.90

We have a sample of 4 forms.

We can use the binomial distribution,

a.) P(None of the order are tagged)

$= P(X=0)$

$= ^4C_0(0.1)^0(0.9)^4$

$= 0.65$

b.) P( less than three tagged order forms)

$= P(X<3)$

$= P(X=0)+P(X=1)+P(X=2)$

$= ^4C_0(0.1)^0(0.9)^4+^4C_1(0.1)^1(0.9)^3+^4C_2(0.1)2^0(0.9)^2$

$= 0.65+0.29+0.004$

$= 0.94$