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 contains errors,the standard deviation of x is ______.

Question

Quizplus · Accepted Answer

The standard deviation of x can be calculated using the formula for the standard deviation of a hypergeometric distribution, which is appropriate here since the sampling is without replacement. The formula is: sqrt[n * (K/N) * (1 - K/N) * ((N-n)/(N-1))], where n is the sample size, K is the number of successes in the population, and N is the population size. Plugging in the values: n = 10, K = 400 (20% of 2000), and N = 2000, the standard deviation is approximately 1.26.