100 random draws from w/ replacement. Sum of draws is 297. Can you estimate te avg. of the numbers in the box (I think yes at 2.97)? Can you give a confidence interval for the estimate (I think no)?

I think you're correct. Certainly your sample mean (2.97) will be your point estimate of the population mean, as you say.

Without further information, though, you can't construct a confidence interval. You don't *always* need a standard deviation to be provided (e.g. you can derive this directly for proportions, since you know each response is 0 or 1), but you need some estimate of the variability.

Is there anything else to the question, or any other information about the variable? All we're told is that they're numbers, but are they real numbers? Integers? Natural numbers (positive integers)? Check - if you're told e.g. the numbers are poisson-distributed, for example, or are all 2s and 4s, or even just that they're all positive integers or some similar bit of information, then you CAN estimate the variability and therefore construct a confidence interval around the mean.