"Normal" precipitation does not equal "what you should expect." "Normal" precipitation to a meteorologist is an average of the precipitation values over a 30-year period. Precipitation may very often be either well above or well below the seasonal average, or "normal."
For example:
In the Nebraska Panhandle, for the month of April, the average or "normal" precipitation is 1.75 inches. However, as you can see in the graph, between 1980 and 2008, the Nebraska Panhandle received about 1.75 inches (+ or - .25 inches) of precipitation in April only five times!
Reference: "Understanding Weather Normals" by Jack Williams, USAToday.com; NDMC "Drought Indices"