Suppose the core temp.(in degrees celsius, when used intensively) of the latest Dell desktop computer is normally distributed with mean 40 and standard deviation 5, while for the latest Compaq it is normally distrbuted with mean 45 and standard deviation 8. Suppose we measure the Dell temperature 20 times (on separate days) and obtain measurements D_1, D_{2, ...,}D_20, and we also measure the Compaq temperature 30 times and obtain measurements C_1, C_{2, ...,}C30.

Identify the distrbution of Dbar =(D_1, D_{2, ...,}D20)/20 and Cbar=(C_1, C_{2, ...,}C30/30) and X=Cbar-Dbar.