Problem $2(22$ points$).$ A process produces rubber belts in lots of size $2,500.$ Inspection records on the last $20$ lots reveal the data the number of nonconforming belts, as shown in the table on the right. The sum of all the nonconforming belts is $6,141.$

Q$2-1(10$ points$).$ Please set up the p$-$chart. Indeed, calculate the UCL, CL$,$ and LCL for $p-$chart.

Q$2-2(5$ points$).$ Based on the p$-$chart you developed in Q$2-1,$ is the process in statistical control? Explain your reasoning.

$\backslash$table$[[\backslash$table$[[$Lot$],[$Number$]],$Number of Nonconforming Belts,$\backslash$table$[[$Lot$],[$Number$]],$Number of Nonconforming Belts$],[1,230,11,456],[2,435,12,394],[3,221,13,285],[4,346,14,331],[5,230,15,198],[6,327,16,414],[7,285,17,131],[8,311,18,269],[9,342,19,221],[10,308,20,407]]$

Q$2-3(7$ points$).$ Lee was ready to move on$,$ but Jay stopped him, suggesting they should set up an np$-$chart. Lee wasn't sure if this was necessary. Do you think setting uptan np$-$chart would provide new or different information? Please explain.