$1.$ The auditors are using mean$-$per unit sampling to evaluate the reasonableness of the book value of the accounts receivable of Mojito, Inc. Mojito has $10,000$ receivable accounts with a total book value of $$1,000,000.$ The auditors estimate the population$$s standard deviation as being equal to $$20.$ After examining the overall audit plan, the auditors believe that the account$$s tolerable misstatement is $$60,000,$ and that a risk of incorrect rejection of $4\mathrm{.}6\%$ and a risk of incorrect acceptance of $5\%$ should be used.

Required:

a$.$ Calculate the required sample size.

b$.$ Now, ignore your sample size calculation in part a$.$ and assume that your answer was a sample size of $150$ and that you obtained the following results:

Average audited value of items in sample $$96$

Average book value of items in sample $$98$

Sample Standard deviation $$22$

Using mean$-$per$-$unit sampling, calculate the projected misstatement for the population.

c$.$ Still using a sample size of $150,$ using mean$-$per$-$unit sampling, calculate the adjusted allowance for sampling risk and use it to form a statistical conclusion concerning the book value of the population $($$$1,000,000).$ That is$,$ calculate an interval and either $$accept$$ or $$reject$$ the client$$s book value.