Problem $3(4$ points$)$

$3$D printers create objects by printing layers of material one on top of the other. Different

materials have different mean thicknesses and standard deviations. A particular part is

made by stacking $10$ layers of material A$,$ followed by $15$ layers of material B$,$ and $30$ layers

of material C$.$ The characteristics of these materials is shown in the table above $($note the

units$).$ Assume that the layer thicknesses are jointly independent. Compute the mean $($in

mm $)$ and standard deviation $($in $m)$ of the total thickness $T$ of the part.

$($please show work$)$