Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc.,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2006. A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors,P(x0)is _______________.

Question

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc.,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2006. A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors,P(x>0)is _______________.

Quizplus · Accepted Answer

The probability that at least one voucher in the sample has errors (P(x>0)) can be found by calculating 1 minus the probability that none of the vouchers have errors. Given that 20% of the vouchers have errors, the probability that a single voucher does not have an error is 0.8. The probability that all 10 vouchers in the sample do not have errors is 0.8^10. Therefore, P(x>0) = 1 - 0.8^10 = 0.8926.