As punishment for bad behavior, the Riddler is put in charge of the meals at Arkham Asylum. Fortunately, he is a bit of a perfectionist and wants to do a great job. He decides to set up a control chart to measure the unsatisfactory meals and surveys the inmates $10$ times. Batman has been very busy so the sample size is $1000$ samples per meal. The following data was collected. Sample $1(83$ bad meals out of $1000),$ Sample $2(54$ bad per $1000),$ S$3(79$ bad per $1000),$ S$4(73$ bad per $1000),$ S$5(60$ bad per $1000),$ S$6(67$ bad per $1000),$ S$7(53$ bad per $1000),$ S$8(35$ bad per $1000),$ S$9(40$ bad per $1000)$ and S$10(62$ bad per $1000).$ Help the Riddler improve the meals by calculating the Upper $($UCL$)$ and Lower $($LCL$)$ control limits for this process.