Also look at the chart on your driver's door jamb (and owners manual)...and the recommended 17" tire size should be listed. The rolling diameter/circumference of all the recommended tires sizes is approx the same...at least within 3% (+/-) each other.
Just think about the 4.6is & 4.8is...they have the small 19" compact tire for the spare...that tire is way smaller than the 315/35/20 rear wheel...but the rolling diameter is the same.
BMW started giving different full spares around the early turn of the century (2000 - 2003 model year)...if you have a full sized spare...it is usually one of the lesser wheels if you have an upgraded size or more popular wheel.