Stringer Size for Decking Stairs

I'm about to build the access stairs to my new raised deck which will go up to approximately 1400 mm and have 8 steps.

The rise will be 180 mm and the going 260 mm and I intend to have three stringers (the width of the stairs will be around 870 mm).

Locally 225 x 47 treated timber seems to be readily available and I was going to use this to cut open stringers from which would leave around 75 mm of timber at the bottom of each cut out. I have seen some pre-cut ones like this but they were only 5 steps high.

On-line a lot of US sites seem to recommend using 12" x 2" timber so my question is will the readily available 225 x 47 be OK or do I really need to source some 300 x 50.

John.