Optimality of Greedy algorithm for minimization Knapsack Problem Given items with weight $w_i$ and profits $p_i$, minimization Knapsack problem is to pick a subset of items $I$, s.t. $\sum_{i\in{I}}{w_i} \geq W$ and $\sum_{i\in{I}}{p_i}$ is minimized.

The greedy algorithm simply sorts items based on ratio $\frac{p_i}{w_i}$. It scans and sum up the sorted items in increasing order, until $\sum{w_i}\geq{W}$. Then outputs $\sum{p_i}$.

If the distribution of $p_i$ is known (say, following zipf distribution) and $w_i$ is randomly distributed, and independently with value of $p_i$, then what is the average optimality ratio which is ratio of $\sum_{i\in{I}}{p_i}$ to the optimal results.

Note: in worst case, this greedy algorithm can be arbitrarily bad, according to 
following book. P412, Knapsack Problems, By Hans Kellerer, Ulrich Pferschy, David Pisinger.
I didn't understand the question very well, but I think you're asking about the ratio of the greedy solution to the optimal solution when the problem instances are taken out of a certain probability distribution. I don't have a theoretic solution to this problem, but if you need the answer for practical reasons, then I think a Monte-Carlo simulation would give reliable results.  You can approximate knapsack to the desired precision using the well-known dynamic programming algorithm to obtain an approximate value of the optimal solution and then compare it to the greedy algorithm. You generate a number of random instances, and see where the ratio usually falls.
In order to have more reliable estimates, you can establish confidence intervals for the fraction of instances whose greedy/optimal ratio falls within a given interval, etc.