If you took 1 mL of mucin solution with a concentration of 20 mg/mL, you would have 20 milligrams of mucin. In a final volume of 10 milliliters, the concentration would be 2 mg/mL. Offhand, I suspect that your calculation has some inconsistency in units

The final concentration (which I take to be 2 µg/mL) is quite a bit smaller than the stock concentration. That means that you will need to pipet a very small volume.