I would guess as well that your bike is from the End of 80ties.
Norco had 1992/93 already nice MTBs like Rampage and a Full suspension.
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Sometimes the low entry level bike looked indeed much older, as cheaper parts and last gen technology is often used.
But also the decals look so 80ties.
I had a while ago a old bush pilot from most likely 1989 with similar decal style as at your Cherokee.
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Obviously early Norco bikes aren't documented well and there is very little information available online.
Maybe those bikes had been also just produced in low numbers and there was not a clear designed range?
According information from an earlier history section at the Norco website, they have started in 1984 to offer MTBs
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Yours is an ATB, also because no cantilever brakes have been used. Still a very nice find
A bit of cleaning and new grips and than have fun and please keep it, it anyhow looks like that there is already someone in your family which wants this bike inherited in a few decades.