  Let K be a d-dimensional convex body, and let $K^{(n)}$ be the intersection
of n halfspaces containing $K$ whose bounding hyperplanes are independent and
identically distributed. Under suitable distributional assumptions, we prove an
asymptotic formula for the expectation of the difference of the mean widths of
$K^{(n)}$ and K, and another asymptotic formula for the expectation of the
number of facets of $K^{(n)}$. These results are achieved by establishing an
asymptotic result on weighted volume approximation of $K$ and by "dualizing" it
using polarity.
