# Probability of Rejecting the Ledger

An auditor takes samples from ledgers to decide whether to certify or reject the ledger. The sampling method used is to select 10 entries at random from the ledgers and then analyze each for errors. If the auditor finds no errors he certifies the ledger. If he finds 2 or more entries with errors he rejects the ledgers. If the auditor finds one entry with errors he takes an additional sample of 20 entries before making a decision. If he finds 2 or more entries with errors in the supplemental sample he rejects the ledger; otherwise he certifies it.

Assume the ledger is fairly decent with errors in only 5% of the entries (for questions 1, 2 and 3).

Determine:

1. The probability of rejecting the ledger.

2. The probability that a supplemental sample will be needed.

3. If the fixed cost of selecting any sample is $500 and the variable cost of analyzing a single entry for errors is $100 what is the expected cost of this sampling plan?

4. If the ledger was poorly done with errors in 15% of the entries, what is the probability that the auditor would certify it?

5. Suppose the auditor has 15 different audits (9 industrial and 6 retail) to do. On the first day he selects 3 companies at random to audit the ledgers. What is the probability that 2 of them are retail companies?

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#### Solution Preview

Please see the attached file for proper formatting.

Section A. Ledger is fairly decent with only 5% errors.

Suppose X denotes the number of entries with errors in the first sample of 10 entries. Clearly X follows binomial distribution with parameters n = 10 and p = 0.05. i.e., . The probability function of X is given by

Suppose Y denotes the number of entries with errors in the second sample of 20 entries. Clearly Y follows binomial distribution with parameters n = 20 and p = 0.05. i.e., . The probability function of Y is given by

1. Rejecting the ledger can happen in two ...

#### Solution Summary

The probability of rejecting the ledger is determined.