You are a supervisor in the Flint, Michigan water quality testing laboratory which performs trace elemental analysis. The usual instrument for the analysis of Pb was being repaired, so your industrious technician devised an alternate method which measures the UV absorption of the Pb:EDTA complex. The technician established that absorbance varied linearly with the amount of Pb $($calibration is linear!$).$ Using the new method, the following absorbance signals $($for $5$ replicate measurements$)$ were obtained for a blank and for a sample submitted for analysis:

Blank Sample $0\mathrm{.}0010\mathrm{.}0050\mathrm{.}0020\mathrm{.}0030\mathrm{.}0000\mathrm{.}0040\mathrm{.}0030\mathrm{.}0050\mathrm{.}0020\mathrm{.}004$

a$)$ Based on the average absorbance obtained for the sample, the technician reported that the water sample contained $250$ ppb Pb $($note that $15$ ppb is the EPA limit$).$ As the laboratory supervisor, you are ultimately responsible for the analysis results that are reported. Should this result be reported? $($Explain the reasoning based on the above data. Hint: this looks like a Signal$-$to$-$Noise issue.$)$

b$)$ To confirm your suspicions, you measured a $1000$ ppb Pb standard that gave an average absorbance signal of $0\mathrm{.}015.$ Given this data and that from above, what is the detection limit in ppb Pb for the method?