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, 2013.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, 2013.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

Since 20% of the population of vouchers contain errors, the sample follows a binomial distribution with n = 10 and p = 0.2. 
P(x > 0) = 1 - P(x = 0) 
= 1 - (0.8)^10 
= 1 - 0.1074 
= 0.8926 
Therefore, the answer is C.