Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1, 2018, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than .06 is closest to ___________.
A)0.4706
B)0.9706
C)0.0588
D)0.9412
E)0.9876

Question

Quizplus · Accepted Answer

The probability that a random sample of 200 vouchers will have a sample proportion greater than 0.06 can be found using the normal approximation to the binomial distribution. Given that 10% of the vouchers have irregularities, the expected proportion of irregularities in any sample is 0.10. The standard error (SE) of the sample proportion is calculated using the formula SE = sqrt[p(1-p)/n], where p is the proportion of interest (0.10) and n is the sample size (200). This gives SE = sqrt[0.10*0.90/200] = 0.0212. To find the probability that the sample proportion is greater than 0.06, we calculate the z-score for 0.06 using the formula z = (proportion - mean) / SE = (0.06 - 0.10) / 0.0212. The z-score corresponds to a probability in the lower tail, and the probability of interest is 1 minus this value. This calculation yields a probability close to 0.9706, indicating a high likelihood of finding a sample proportion greater than 0.06.