$(1)$ A $10$ mL sewage sample was diluted with distilled water $($BOD$5=0)$ to fill a $300$ mL BOD$-$testing bottle. The initial DO of the mixture is $9\mathrm{.}0$ mg$/$L$.$ Your boss told you to keep the drop of DO between $30\%$ and $70\%$ of the initial DO$,$ to assure the accuracy of the BOD test. Please estimate the range of the sewage sample$$s BOD that can be accurately tested using this method.

$(2)$ If distilled water is unavailable and tap water $($BOD$5=2$ mg$/$L$)$ must be used instead, please re$-$estimate the range of BOD that can be accurately tested.