An auditor inspects $25$ transactions processed by the business office of a company. The auditor selects these transactions at random from the thousands that were processed in the most recent three months. In the$$ past, the auditor has found$10\%$ of transactions at this type of company to have been processed incorrectly$($including such errors as wrong$$ account, incorrect budget$$ code, and incomplete$$ records$).$ Mark the following statement as true or false. If you believe that a statement is$$ false, briefly explain why you think it is false.

It would be unlikely for the auditor to discover more than $10$ errors among these transactions because such an event lies more than $4$ SDs above the mean.

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Part $1$

Choose the correct answer below.

A$.$

The statement is true.

B$.$

The statement is false. Finding $10$ errors is more than $4$ SDs below the$$ mean, so the auditor is very unlikely to find more than $10$ errors.

C$.$

The statement is false. Finding $10$ errors is within $1$ SD of the$$ mean, so finding more than $10$ errors would not be an unusual result.

D$.$

The statement is false. Finding $10$ errors is more than $4$ SDs above the$$ mean, so the auditor is almost certain to find more than $10$ errors.