Sampling Distributions · Challenge problem

A machine fills cans with SD $6$ mL. Every hour $9$ cans are measured, and the machine is recalibrated if the sample mean is more than $k$ mL away from the target $250$ mL. When the machine is working correctly (mean $250$, fill roughly normal), a recalibration should happen only about $1.24\%$ of the time. Find $k$.