How do I know if I need a new Oxygen Sensor???

I have a 1985 BMW 735i that has been running a little rough lately and today it started sputtering and I can't hardly keep it running. Someone told me it could be the oxygen sensor. I called and got a price of $120 for a new sensor. Before I gamble that much money, I thought I would try my luck here. My questions to the forum are: How do I know if my old oxygen sensor is bad? Also, where is it located on the E23 model (3.5L) and is it hard to replace? If I spend that much money on a part only to find out it wasn't my problem, I'll be sick. Thanks for your help!!!

Do not know about 1985, but in 1988 the o2 sensor prompt came up on instrument cluster. The sensor on the 735 is on top of the exhaust pipe near cat convertor and you must lower the exhaust system sufficiently to access the sensor. The sensor only works with a hot engine/exhaust and if it fails is does go to full rich mixture setting