A construction worker was exposed to $85$ dB for $2$ hrs$,89$ dB for $2\mathrm{.}5$ hrs$,93$ dB for $3$ hrs and $90$ dB for $0\mathrm{.}5$ hrs$.$ What was the total noise dose over the $8$ hours and was the worker overexposed per OSHA standard? You must show your calculation process and include appropriate unit for full credits.