A textbook publishing company has compiled data on total annual sales of its business textbooks for the preceding eight years:

Year: $12345678$

Sales$(000)$: $37\mathrm{.}6042\mathrm{.}4049\mathrm{.}3053\mathrm{.}4055\mathrm{.}2057\mathrm{.}7060\mathrm{.}8069\mathrm{.}20$

a$-1.$ Select the correct data chart and fit an appropriate model to it$.$

Chart A Chart B Chart C

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a$-2.$ Forecast the preceding eight years, and determine the forecast errors. $($Negative answers should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$

Year Sales$(000)$ Forecast Error Error$\backslash$Lambda $2$

$137\mathrm{.}60$

$242\mathrm{.}40$

$349\mathrm{.}30$

$453\mathrm{.}40$

$555\mathrm{.}20$

$657\mathrm{.}70$

$760\mathrm{.}80$

$869\mathrm{.}20$

a$-3.$ Construct $2$s control limits$.($Round the final answer to $2$ decimal places.$)$

$2$s control limits are $\backslash$pm

b$.$ Using the model, forecast textbook sales for each of the next five years. $($Round the final answers to $1$ decimal place.$)$

Year Sales$(000)$ Forecast Error

$974\mathrm{.}70$

$1077\mathrm{.}20$

$1184\mathrm{.}10$

$1288\mathrm{.}50$

$1391\mathrm{.}50$

c$.$ Suppose actual sales for the next five years turn out as follows:

Year: $910111213$

Sales$(000)$: $74\mathrm{.}7077\mathrm{.}2084\mathrm{.}1088\mathrm{.}5091\mathrm{.}50$

Calculate the forecast errors for years $9$ to $13.$ Is the forecasting process in control?

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