  For a given convex body K in $R^d$, a random polytope $K^{(n)}$ is defined
(essentially) as the intersection of $n$ independent closed halfspaces
containing $K$ and having an isotropic and (in a specified sense) uniform
distribution. We prove upper and lower bounds, of optimal orders, for the
difference of the mean widths of $K^{(n)}$ and K, as n tends to infinity. For a
simplicial polytope P, a precise asymptotic formula for the difference of the
mean widths of $P^{(n)}$ and P is obtained.
