Question

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. If 10% of the 5,000 payroll vouchers issued since January 1, 2000, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than .06 is ___________.a.) 0.4706b.) 0.9706c.) 0.0588d.) 0.9412e.) 0.9876

Answer 1

Answer: b.) 0.9706

Explanation:

Given : Proportion of the 5,000 payroll vouchers issued since January 1, 2000, have irregularities : p=0.10

Now , using standard normal z-value table , we have

The probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than .06 will be :-

`P(z>\frac{0.6-0.10}{\sqrt{(0.10(1-0.10))/(200)}})\ \ [\because z=\frac{\hat{p}-p}{\sqrt(p(1-p))/(n)}}]\\\\=P(z> -1.89)\\\\=P(z<1.89)\ \ [\because P(Z>-z)=P(Z<z)]\\\\=0.9706` [By using z-value table]

Hence, the probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than .06 is b.) 0.9706.