Depends on what you consider a 'conversion'. Is entering an email address to sign up for a free newsletter a 'conversion'? Or does it have to be a revenue producing event? The first will have a much higher rate than the 2nd, obviously.
One thing I can tell you (since I have seen the numbers for a dozen different companies that do this) is the conversion rate from a 2-week or 30-day free trial to a paying user of the service averages around 50%. ie half the people who take a free trial of a service will end up paying for that service. The numbers range from 40% to 60%. It'll be higher if you ask for more info up front (because you end up filtering out the lookyloos who aren't serious if you ask for more info at the start of the free trial).
What I do not have great data for is the conversion rate from first-time-visitor to free-trial (or revenue-event). I have anecdotes that tell me it's low single-digits (2% to 5%). If you're talking about a 15% conversion rate from first-time-visitor to revenue-event then that seems high (unless you're selling Lady Gaga concert tickets or something). Those numbers are usually very proprietary and I'd be surprised (and interested in) if you find any solid data on them...