The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past $5$ years are as follows:

$\backslash$table$[[$Year$,1,2,3,4,5],[$Mileage$,3,050,3,950,3,450,3,750,3,800]]$

a$)$ Using a $2-$year moving average, the forecast for year $6=3,775$ miles $($round your response to the nearest whole number$).$

b$)$ If a $2-$year moving average is used to make the forecast, the MAD based on this $=100$ miles $($round your response to one decimal place$).($Hint: You will have only $3$ years of matched data.$)$

c$)$ The forecast for year $6$ using a weighted $2-$year moving average with weights of $0\mathrm{.}45$ and $0\mathrm{.}55($the weight of $0\mathrm{.}55$ is for the most recent period$)=$ response to the nearest whole number$).$