slickdeals...also, the nosing provides a visual distinction so that negotiating the stairs, particularly walking down the stairs is easier for some. Primary reason is to prevent slipping.
GTR1--I'm confused by your dimensions. The nosing does not have a "thickness". It is the leading 1-inch of a tread width. The Florida Building Code references NFPA 101, The Life Safety Code. That gives the dimensions and requirements for treads, risers, stairs in general, and handrails/guardrails. The FBC also addresses some of these items and there is some conflict. Check both for your guidance.
NFPA 101,for existing buildings, gives a maximum riser height of 8 inches and a minimum tread width of 9 inches.
In general, the sum of two risers and a tread should be between 24 and 25 inches. As you can see, if you have two 8-inch risers and a 9 inch tread, you are at 25 inches.
What was the prevailing building code in effect at the time of construction for your project? For the FBC versions 2001 thru 2007, the risers must be between 4 and 7 inches and the minimum tread width is 11 inches. The 2007 FBC provides some slope tolerances as well (1" in 50")