Does anyone know if this is the right thickness for this coin or is it suppose to be on something else. I can't find any that are this thick in my collection that are around this year.
IMO your cent looks like it was struck slightly off center. Sometimes coins are struck on slightly thick or slightly thin planchets. It would be helpful if you could give us the weight of the coin.
Normal weight is 3.11 grams. your coin is within tolerance limits. Could you post a photo of the edge. If the edge is very thick you might have a spooned coin.
Thickness tolerance = 1.52 mm -0.102/+0.152 mm Since the weight is within tolerance, I would expect thickness also to be within tolerance. It could be a slightly tapered planchet - check to see if the rim varies in thickness, or measure the rim at 4 places around the circumference with calipers in mm to 2 decimals.
Thinner than normal thickness can occur on any Lincoln cent minted before mid 1982. But yours is within tolerance. http://www.error-ref.com/rolled-thin-planchets/ Yours seems to also have some circulation wear which would add the the lesser than normal weigh. It's a 100 year old Cent!