ALT OVERSHOT; A CL65 FLT CREW OVERSHOOTS THEIR ASSIGNED MISSED APCH ALT WHEN RECOVERING FROM WINDSHEAR ENCOUNTERED ON FINAL APCH INTO DTW.

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