Question

You are a graduate auditor at EY and you’ve been asked by your manager to verify the accuracy of 4 invoices issued by a client firm which EY is auditing. Your manager informs you that, based on prior year audits, the probability of an invoice being accurate is 60%.

a.Which method for assigning probabilities has your manager used in his estimation?(1 mark)

b.What is the probability that exactly 1 of the 4 sampled invoices is accurate?(1mark)

c.State one assumption which underlies your calculation in part (b). Hint: There are several to choose from.(1 mark)

d.What is the probability that at least two of the sampled invoices are accurate? e.Using the probabilities calculated above and/ orotherwise, graphthe PDF which applies to your sample of invoices. Hint: Ensure that your PDF is complete and is in line with best principles for the visual presentation of statistical information.

Answer 1

a.

Since the manager has used historical data (prior year audits) to assign probabilities we can say that he has used the relative frequency method to assign probabilities.

b.

Let X denote the number of accurate invoices out of the 4 invoices selected for the audit.

Now, the probability of each invoice being accurate is 0.60.

Thus, X ~ Binomial(n = 4, p = 0.60); and the pmf of X is given by:

Now, the probability that exactly 1 of the 4 sampled invoices is accurate is given by:

c.

Any one of the assumptions of the Binomial distribution will be an answer to this question. One of the assumptions is :
The probability of an invoice being accurate is independent of the other invoices. Moreover, the probability of an invoice being accurate is same for all invoices.

d.

The probability that at least two of the sampled invoices are accurate is given by:

e.

The graph of the pmf of X ~ Binomial(n = 4, p =0.6) is given by:

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