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 contains errors, the standard deviation of x is ______.
A)1.26
B)1.60
C)14.14
D)3.16
E)0.00

Question

Quizplus · Accepted Answer

The standard deviation of x, denoted as σx, in a binomial distribution can be calculated using the formula σx = sqrt[n*p*(1-p)*(N-n)/(N-1)], where n is the sample size, p is the probability of success (in this case, finding an error), and N is the population size. Given n=10, p=0.20 (20%), and N=2000, substituting these values into the formula gives σx = sqrt[10*0.20*(1-0.20)*(2000-10)/(2000-1)] = sqrt[10*0.20*0.80*1990/1999] ≈ 1.26.