I have a blood pressure in the range of 160/110 on average yet my pulse rate is always between 60 and 75 is this normal?

BP too high: Normal is less than 140/90 see your doctor to have this checked and treated.Left untreated, you are at risk for premature ( at a much earlier age than normal) heart attacks and strokes.In other words, irreversible heart and brain damage and death.

Define "this": It's normal that hr is unaffected by even severe blood pressures. In fact, paradoxically, at very high blood pressures, low heart rate can develop for reasons that don't particularly matter (it's a reflex arc). What's not normal is a top number of 160 (systolic) and bottom (diastolic) of 110. If this is a reproducible finding, you have stage 2 hypertension and need to be on a few BP meds.