The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years, 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts.
-What is the probability that at least 30 accounts will be classified as delinquent?
A)0.3186
B)0.1814
C)0.8186
D)0.6372
E)0.7584

Question

Quizplus · Accepted Answer

The probability of at least 30 accounts being delinquent can be found using the normal approximation to the binomial distribution. Given the historical delinquency rate of 14% (p = 0.14), for n = 250 accounts, the expected number of delinquent accounts is np = 35. The standard deviation is sqrt(np(1-p)) = sqrt(250*0.14*0.86) ≈ 5.7. To find the probability of at least 30 being delinquent, we calculate the Z-score for 29.5 (using continuity correction) and find the probability to the right of this Z-score. The calculation leads to a probability that matches closest to option C, indicating that it is the correct choice. This approach approximates the binomial distribution with a normal distribution due to the large sample size.

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