Question

In: Statistics and Probability

Discrete R.V and Probability Distribution

In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 5% of the time. Suppose that an auditor randomly checks three entries.

(a) Find the probability distribution for X , the number of errors detected by the  auditor.

(b) Find the probability that the auditor will detect more than one error.

 

Solutions

Expert Solution

Solution

(a) Find the probability distribution for X , the number of errors detected by the auditor

\( X\sim Bin(3,0.05) \hspace{2mm} , P=0.05 \)

so , \( P(X=x)=C_n^xP^x\left(1-P\right)^{n-x}\hspace{2mm},n=3 \)

                         \( =C_3^1P^x\left(1-P\right)^{3-x} \)

Then \( P(X=0)=(1-P)^3=(1-0.05)^3=0.857375 \)

         \( P(X=1)=3\times 0.05\times (1-0.05)^3=0.135375 \)

         \( P(X=2)=3\times(0.05)^2\times (1-0.05)=0.007125 \)

         \( P(X=3)=(0.05)^3=0.000125 \)

(b) Find the probability that the auditor will detect more than one error.

\( \implies P(X>1)=P(X=2)+P(X=3)=0.007125+0.000125=0.00712 \)


Therefore.

a).

b). \( P(X>1)=0.00712 \)

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