DNS Query Question

[Dennis Dayman <dennis () thenose net>]

I have a customer having some DNS issues. They have done some research
regarding some DNS timeout errors they saw with Verizon's sender verify
looking up their MX records. What they have discovered is their current 
DNS service has a 1% failure/timeout rate. They are exploring other 
vendors (UltraDNS for one), but need an estimate of the number of DNS 
queries for accurate pricing to put together a ROI argument for the
switch.

I have no IDEA if this can be determined, but what is a good estimate of
the number of DNS queries generated from sending an email? I know that
it may differ from ISP to ISP, but they just need a rough number for
pricing purposes.

If you also happen to know how many DNS requests make it to the root
server (rather than a cached proxy out on the net), that would be great.

-Dennis