It is not entirely clear on what you are trying to measure. Standard deviation is typically used to measure confidence (and report errors, etc.) in a statistical calculation. And so to divide one quantity (range) by another (standard deviation of price) is kind of like dividing a number by a color. Consider some other indicators, like Bollinger Bands, as mentioned, where you have the average value +/- n*std. deviations, which is a valid way to present a statistical measurement. About using standard deviation to represent the probability of all values (even those not measured yet) falling within certain percentages of the mean, this is only valid for normal distributions (and these are ~68%, 95%, and 99.7%, not the other mentioned values), as was indicated. Stock-price distributions are not normally-distributed (they have fat tails), and so this doesn't apply. You can still calculate a variance (and standard deviation), but you can't make the same confidence claims as before.
It just occurred to me that what you meant by range is probably the max. of your measured data minus the min., and not something like the true range (indicator), which is what I was thinking when I posted. I take back my dividing a number by a color remark.
1) At the risk of sounding "simplistic" and maybe not completely understanding what you're asking, if R tends to "exceed" S, you want to be "long" option premium versus the underlying instrument ..... I think. Other quant-nerds can chime in if they want to. 2) If S tends to "exceed" R, you want to be "short" option premium versus the underlying ...... I mostly think so.
You are asking how the price range (high-to-low) over the entire lookback period compares with the price variance (close-to-close) for each price bar. I think we can say that the more uniform and flat (non-trending) the price series is, the closer R will be to S and the ratio (R/S)will be smaller. I don't think this is useful for anything in particular unless you are scanning to identify markets that are flat with uniform volatility.