An audit of a large chain of departmental stores involves checking a probability sample from a population of 2115 customer accounts that have outstanding layby account balances. A frame of customer accounts is given in the Excel file A_S1_16_1 a) Select a systematic sample of 185 accounts. b) What is the probability that the mean outstanding credit balance of the 185 accounts selected in Part (a) is less than $450. Comment on you answer. c) What sample size would be required for the auditors to be approximately 95% confident that their estimate of the mean outstanding layby balance of the customer accounts is within $80 of the true mean? d) Choose a simple random sample of the size found in Part (c). e) Compute the observed sample error based on the sample you have drawn in Part (d). How does this actual sampling error compare to the maximum allowable sampling error specified in Part (c) f) Explain what sampling design could be used to ensure that the selected sample of accounts could better represent the population. g) i) Use your sample from a) to determine and interpret a 99% confidence interval estimate of the proportion of accounts that have outstanding layby balances less than $300. ii) Does the corresponding population proportion lie in the confidence interval obtained in Part g (i)? Explain why or why not.