$607$Questions and Problems$0\mathrm{.}355$ inches in diameter, but there is some variation in its output. Provided that the machine isproducing rods within $0\mathrm{.}353$ to $0\mathrm{.}357$ inches in diameter, its output is considered acceptable orwithin control limits$.$ Management uses a control chart to track the diameter of the rods beingproduced by the machine over time so that remedial measures can be taken if the machinebegins to produce unacceptable rods. Figure $11\mathrm{.}46$ shows an example of this type of chart.FIGURE $11\mathrm{.}46$Graph for rodmanufacturingproblemUnacceptable rods represent waste. Thus, management wants to develop a procedure topredict when the machine will start producing rods that are outside the control limits$,$ so thatappropriate actions can be taken to prevent the production of rods that must be scrapped. Ofthe time series models discussed in this chapter, which is the most appropriate tool for thisproblem? Explain your answer$\mathrm{.}3.$ Each month, Joe$$s Auto Parts uses exponential smoothing $($with a $50\mathrm{.}25)$ to predict thenumber of cans of brake fluid that will be sold during the next month. In June, Joe forecastthat he would sell $37$ cans of brake fluid during July. Joe actually sold $43$ cans in July.a$.$ What is Joe$$s forecast for brake fluid sales in August and September?b$.$ Suppose that Joe sells $32$ cans of brake fluid in August. What is the revised forecast forSeptember?Questions $4$ through $10$ refer to the data in the file that accompanies this book named Small$-$Business.xlsx representing annual sales $($in $$1,000$s$)$ for a small business. $5.$ Compute the two$-$period and four$-$period moving average predictions for the data set.a$.$ Prepare a line graph comparing the moving average predictions against the original data.b$.$ Do the moving averages tend to overestimate or underestimate the actual data? Why?c$.$ Compute forecasts for the next $2$ years using the two$-$period and four$-$period movingaverage techniques.