SQL Server - Shuffle results randomly, but with a weight assigned to each record

I know that the normal way to shuffle results with SQL Server is to order by NEWID(), except I'd like to instead use a weighted shuffle.

Each recor开发者_JS百科d in my table has an integer 'Importance' from 1 to 10. I'd like to order by RAND()*Importance, except SQL Server has RAND() return the same value for each record returned.

Any ideas please?

Take a look at SQL Server - Set based random numbers for some ideas