Question

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 120 days overdue. The historical records of the company show that over the past 10 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?

18.14

81.86

31.86

75.84

63.72

Answer 1

ANSWER:

Given

n = 250

p = 14% = 0.14

Mean(μ) = np

μ = 250×0.14 = 35

Standard deviation(σ)=$\small \sqrt{np(1-p)}$

$\small \sigma =\sqrt{250*0.14(1-0.14)}$

σ = 5.4863

probability that at least 30 accounts

P(X $\small \leq$ 30)

< 30 – 35 5.4863

P(Z $\small \leq$ -0.9114)

= 0.1814

= 18.14%

The probability that at least 30 accounts will be classified as delinquent is 18.14

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