Some people say there is no such thing as a low blood pressure.Some even insist that low blood pressure indicates excellent health. But the more common belief is that blood pressure below the normal range of 120/80 may result in fatigue and weakness, though this has yet to be proven in the world of medicine. Blood pressure in the normal range is rare. Either the systolic or the diastolic reading is liable to show lesser than the normal range in  most individuals.