First of all, you're probably looking at the way the lens is rated. Lens ratings for a zoom lens show the maximum aperture (smallest f/stop number). The first number is the maximum aperture at full wide angle, and the second number is the maximum aperture available at full zoom.
The Z2 lens is rated at F/2.8 - F3.7.
You usually have a smaller aperture (larger F/Stop Number) available at full zoom, because less light can reach the sensor through the lens when using zoom. So, the smaller the F/Stop Numbers (larger the aperture ratings), the better when comparing lenses.
The smallest aperture available on the Z2 is F/8
The reason you don'tneed Apertures smaller than around F/8 on consumer (non-DSLR) Digital Cameras is because you have far greater depth of field, for a given 35mm equivalent focal length and aperture setting; compared to a 35mm SLR.
This is because the size of the CCD (sensor) in a Digital Camera, is much smaller than 35mm film. As a result, a much shorter focal length lens can be used, to get the same 35mm equivalent focal length. This is because the image circle can be much smaller, too.
The lens in your Z2 has an actual focal length of only 6.3-63mm (to give it a 35mm equivalent focal length of 38-380mm).
Note that Depth of Field depends on the
Actual (not 35mm equivalent) Focal Length of the lens, Aperture, and Distance to Subject.
So,it has more depth of field for the same subject distance and aperture, and 35mm equivalent focal length (because the actual focal length determines Depth of Field). As a result, you'll have more depth of field at F8 using the Z2, than you would at F16 with a 35mm SLR -- for the same 35mm equivalent focal length.
To get an idea of how aperture, focal length and distance to subject impact depth of field, use this handy online calculator.
It supports popular film and digital camera models, and calculates DOF using true (versus equivalent) focal length, aperture and distance to subject (make sure to use the actual versus equivalent focal length of the camera's lens).
http://dfleming.ameranet.com/dofjs.html
Note that the downside to a consumer (non-DSLR) Digital Camera, is that some users complain that they have too much depth of field (making it more difficult to deliberately blur backgrounds, to help subjects "stand out" more).