If you could plausibly go 20 minutes without receiving an order, this isn't a question about statistics, it's a question about PR.
Moreover, the kind of place that doesn't take an order more than every few minutes probably doesn't pay someone to be on call at 3am.
And what does the marketing department have to do with this? How is that I am running a web site that is important enough to wake me at 3am because someone isn't sure if there's a problem, yet we don't have any operations people who know the normal working of the system well enough to make the call on when something is broken?
Like most contrived examples of how "important" statistics is in software development, IME, yours makes no sense when considered in a realistic context.
You are thinking of including 30 days of toll free phone support with your next product, and have calculated that for this to work out financially you will need less than 1% of your customers to call support.
Again, in any realistic scenario, that little "to work out financially" probably involves far more complicated considerations than some basic probability distribution, and if this choice is being made by a random programmer based on a simplistic model then you're doing it wrong.
You are thinking of including 30 days of toll free phone support with your next product, and have calculated that for this to work out financially you will need less than 1% of your customers to call support. How do you figure out from the record of bug discovery and severity in your testing group's bug tracker if your testing program the probability that your product as it stands is good enough to meet that requirement, and how do you determine how confident you should be of that result, if you do not know anything about probability and statistics?