For Gardyloo Manufacturing,the true proportion of accounts receivable with some kind of error is 0.20.If an auditor randomly samples 225 accounts receivable,what is the approximate normal probability that 39 or fewer will contain errors?
A)0.1797
B)0.2097
C)0.1587
D)0.0544

Question

Quizplus · Accepted Answer

The correct answer is A.The probability of an account receivable containing an error is 0.20. The probability of not containing an error is 1 - 0.20 = 0.80. The probability of 39 or fewer accounts receivable containing errors is the same as the probability of 186 or more accounts receivable not containing errors. The probability of 186 or more accounts receivable not containing errors is the same as the probability of 185 or fewer accounts receivable containing errors. The probability of 185 or fewer accounts receivable containing errors is the same as the probability of 185 or fewer successes in 225 independent trials, each with a probability of success of 0.20. This probability can be approximated by the normal distribution with mean 225 * 0.20 = 45 and standard deviation sqrt(225 * 0.20 * 0.80) = 12.25. The probability of 185 or fewer successes is the same as the probability of a z-score of (185 - 45) / 12.25 = -2.16 or less. The probability of a z-score of -2.16 or less is approximately 0.1797.

For Gardyloo Manufacturing,the True Proportion of Accounts Receivable with Some