What is bright to the human eye, is not to the camera's lens. Chances are, your "well lit" factory only has an EV (Exposure Value) of around 6 or 7.
Also,as a general rule, you want to use a shutter speed of 1/focal length or faster. In other words, if shooting at100mm equivalent zoom, you'll want a shutter speed of around 1/100 second -- just to help reduce blur from camera shake. When using flash, slower shutter speeds can be used, because the flash is freezing the action. So, keeping the camera at nearer to full wide angle can help a little.
You can increase ISO speed to help compensate (but this increases noise).
For example: if shooting near wide angle for your lens, at ISO 100, with an Aperture of around F2.8, you'd need a shutter speed of around 1/8 second at EV 6 to insure proper exposure. This is too slow to prevent blur - even at full wide angle. If you're trying to shoot at ISO 50, the problem will be even worse (because you'd need an even slower shutter speed of about 1/4 second to get proper exposure).
Your Z2'swidest aperture at wide angle is F2.8
Here is a useful chart. Again, what your eyes tell you is bright (indoors), is not to a camera. Note that this chart is based on ISO 100. So, each time you double the ISO speed (settable in camera), you can also double the shutter speed. However, increasing ISO speed will add noise to the photo.
Note that there are a couple of products that can be used to reduce noise, should you decide that increasing ISO speed is the only way to get shutter speeds fast enough for proper exposure without too much blur from camera shake. Noise Ninja and Neat Image are probably the best two. Here are the download links:
[edit - download links corrected]