Data collected on the yearly registrations for a Six Sigma seminar at the Quality College are shown in the following table:

$\backslash$table$[[$Year$,1,2,3,4,5,6,7,8,9,10,11],[$Registrations $(000),5\mathrm{.}0,5\mathrm{.}0,3\mathrm{.}0,6\mathrm{.}0,11\mathrm{.}0,9\mathrm{.}0,7\mathrm{.}0,9\mathrm{.}0,13\mathrm{.}0,16\mathrm{.}0,17\mathrm{.}0]]$

This exercise contains only parts a and $b.$

a$)$ Using a $3-$year moving average, the forecasted registrations $($in thousands$)$ for years $4$ through $12$ are $($round your responses to one decimal place$)$:

$\backslash$table$[[$Year$,4,5,6,7,8,9,10,11,12],[$Forecast$,4\mathrm{.}3,4\mathrm{.}6,6\mathrm{.}6,8\mathrm{.}7,9,8\mathrm{.}3,9\mathrm{.}6,12\mathrm{.}6,15\mathrm{.}3]]$

b$)$ Using a $3-$year weighted moving average in which the registrations in the most recent year are given a weight of $2,$ and registrations in the other $2$ years are each given a weight of $1,$ the forecasted registrations $($in thousands$)$ for years $4$ through $12$ are $($round your responses to one decimal place$)$:

$\backslash$table$[[$Year$,4,5,6,7,8,9,10,11,12],[$Forecast$,,,,,,,,,]]$