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 contains errors, the standard deviation of x is ______?

Answer 1

Answer: 17.89

Step-by-step explanation:

In binomial distribution, the standard deviation is given by :-

$\sigma=\sqrt{np(1-p)}$

As per given , we have

The number of vouchers in the sample with errors is denoted by x.

p= 0.20  , n = 2000

Then , $\sigma=\sqrt{2000\times(0.2)(1-0.2)}$

$\sigma=\sqrt{320}=17.88854382\approx17.89$

Hence, the standard deviation of x is 17.89.