Component has a x% tolerance: What does this mean exactly?
Components are usually tested for datasheet specifications, and parts outside the specification are rejected.  So the distribution may be a truncated normal distribution, or a normal distribution well within the specified limits, depending on the manufacturing process.

So you will never see a 1% resistor with a value outside the 1% specification.

Sometimes parts are binned, with the 1% resistors going into the 1% bin, and ones outside that going into (e.g.) the 5% bin.  So you wouldn't see any 5% parts that were within 1%.  This is less common for many parts mainly because manufacturing tolerances are much better than they used to be, so (for example) the 1% line often runs well within 1% without any outliers.  (Or as a minimum the yield is so high that it's not worth binning.)