Random award question

Question

I'm assisting with the design of an algorithm over the next week to fit the following use case:

A person walking in a store has a tablet and approaches possible customers to notify them of a competition. When a customer enters their details, upon completion of the form - a request is sent to the server, and the customer will be randomly drawn (at that point in time) for a prize.

A maximum of 4 customers are chosen, the number of customers walking into the store is not known. The store is open from 8am until 4pm.

Would there be any other way (other than the ones stipulated) to solve something like this without knowing the average customers visiting the store?

Solution 1

I was thinking a normally distributed probability is used, where the parameters could be tweaked over time to fit this allowing customers to be selected (more or less) equally through out the day.

Solution 2

Similar to solution 1, but the time throughout the day is partitioned into segments. Between the hours of 8am and 12pm, a maximum of 2 people can be chosen.

I don't quite like the idea of doing this because if a majority of the customers come in the morning, this could lead to less than the 4 prize hand out expected of the day.