An audit client has an inventory of 10,000 head of beef cattle (steers). The steers were purchased at various dates and varying prices. In view of the dollar amounts involved, \(\$ 150,000\) is considered to be a material amount, and a 95 percent confidence level is deemed to be necessary. Internal control effectiveness is 85 percent and the effectiveness of supplementary audit procedures is 15 percent. Ultimate risk is 0.05 . The estimated standard deviation of the population is \(\$ 110\). The book value is \(\$ 2,860,000\).

Required:

a. Compute sample size.

b. Without prejudice to your answer in

(a) assume a sample of 200 totaled \(\$ 56,000\) with a standard deviation of \(\$ 102\). Is the account fairly stated?