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

Year: $12345678$

Sales$(000)$: $37\mathrm{.}0043\mathrm{.}1047\mathrm{.}6050\mathrm{.}9055\mathrm{.}5057\mathrm{.}5063\mathrm{.}9067\mathrm{.}80$

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 $2$

$137\mathrm{.}00$

$243\mathrm{.}10$

$347\mathrm{.}60$

$450\mathrm{.}90$

$555\mathrm{.}50$

$657\mathrm{.}50$

$763\mathrm{.}90$

$867\mathrm{.}80$

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

$974\mathrm{.}30$

$1076\mathrm{.}00$

$1183\mathrm{.}20$

$1287\mathrm{.}30$

$1392\mathrm{.}50$

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

Year: $910111213$

Sales$(000)$: $74\mathrm{.}3076\mathrm{.}0083\mathrm{.}2087\mathrm{.}3092\mathrm{.}50$

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

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