(a) A business analyst Wants to construct conndence interval lor the population total, T, based on a simple random sample of size n = 60 drawn from a population with size V = 12,000. The characteristic being observed is assumed to be normally distributed. i. Recommend a suitable estimator of T and provide the formula for computing a 99% confidence interval for T. You should also state the expected value and standard error of the estimator of T. The analyst also wants to construct a 95% confidence interval for the standard deviation, o, of the population. il. Recommend a suitable estimator of o and provide the formula for computing a 95% confidence interval for o. (b) A wholesaler wants to use simple exponential smoothing to predict monthly sales. At the end of January, the wholesaler's forecast for March sales was 11,000. In February, 15,000 units were sold, and during March 19,000 units were sold. i. At the end of March, what is the wholesaler's forecast for the total number of units which will be sold during the following May and June? Use a smoothing constant of 0.25. in. If the value of 0.25 for the smoothing constant could be changed, briefly explain how a different value could be determined. (c) Suggest, with reasons, your recommended time series model for forecasting: i. gas demand i. a stock market index