You are the auditor of Unet Incorporated, an auto air$-$conditioner service and repair company, and you have decided to use the mean$-$per$-$unit method to test the existence and gross valuation of recorded accounts receivable. The client$$s records include $16,500$ accounts with a total book value of $$4,112,000.$ You decide to use tolerable misstatement of $$182,000,$ an incorrect acceptance risk of $5$ percent, and an incorrect rejection risk of $4\mathrm{.}6$ percent. Using Excel, you estimated the standard deviation of the population as $$126.$

Required:

a$.$ Determine the sample size.

b$1.$ The mean audited value of the accounts in the sample was $$244.$ Assuming that the standard deviation of the sample$$s audited value is also $$126,$ what is the projected misstatement for the population?

b$2.$ Will you accept this account as not being materially misstated?

c$1.$ Assuming that the standard deviation of the sample$$s audited value is $$244,$ what is the projected misstatement for the population?

c$2.$ Will you accept this account as not being materially misstated?