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, 2016.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, 2016.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 contains errors (P(x>0)) can be found by subtracting the probability that none of the vouchers in the sample contain errors from 1. Given that 20% of the vouchers contain errors, the probability that a voucher does not contain errors is 80% or 0.8. For a sample of 10 vouchers, the probability that none contain errors is $0.8^{10}$. Therefore, $P(x>0) = 1 - 0.8^{10} = 1 - 0.1073741824 = 0.8926258176$, which rounds to 0.8926.