ACTUALLY Scrupulus is correct! The magic 8 ball uses a random number generator to select it's answer...the same random number generator can be applied to your idea.
If you know an EE the solution to this is EASY. You need: A low power processor with a built in clock, a way to program it, and a motor controller - preferably with a digital input of some sort, oh and 3 motors, one for each wheel/cylinder.
The chip would have to be programmed to generate 3 random codes, with minimum and maximum values mapped to your desired range. The outputs would then be sent to each motor controller. The motor would accelerate based upon the output of the motor controller.
If you're new to this world, but aren't afraid to do a little coding and wiring then you can build a prototype easily by:
1) Get a parallax board. Stamp Basic is very easy to program in and ideal for quick prototyping. The draw back is that the board is not very powerful and can't easily simulate complex circuits...like a cell phone for instance. This draw back is not relevant here.
2) Buy a dozen or so transistors (they're easy to burn up)
3) Get some 20 gauge *solid* wire or whatever is appropriate for your board.
4) Program a random number generator into the board so that the output varies from .2 seconds to 2 seconds of "ON" to say pin 1. I seem to remember the manual telling you how to do this and giving code examples.
5) Take the output of pin 1 and send it to the "enable" input of a transistor...check that polarity is correct. A little puff of smoke means it wasn't.
6) Connect ground to the input of the transistor assuming it is the NPN type and not PNP.*
7) Connect the output of the transistor to the motor.
Connect the free terminal of the motor to + assuming NPN was used.
9) Test: Run the program...works, yay.
10) Code the program to run based upon [button] input. Again the manual tells you how to do this and gives code examples.