You are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food$-$service department. You conducted a $10-$day survey by submitting a simple questionnaire to the $400$ patients with each meal, asking that they simply check off that the meal was either satisfactory or unsatisfactory. For simplicity in this

$\backslash$table$[[,\backslash$table$[[$NUMBER OF$],[$UNSATISFACTORY$],[$MEALS$]],\backslash$table$[[$SAMPLE$],[$SIZE$]]],[$December $1,60,1,000],[$December $2,52,1,000],[$December $3,40,1,000],[$December $4,65,1,000],[$December $5,54,1,000],[$December $6,38,1,000],[$December $7,64,1,000],[$December $8,61,1,000],[$December $9,57,1,000],[$December $10,63,1,000],[,554,10,000]]$

a$.$ Determine the $\frac{?}{\text{b}\text{a}\text{r}}(p),S_p,$UCL, and $LCL$ based on the questionnaire results, using a confidence interval of $95\mathrm{.}5$ percent, which is two standard deviations.

Note: Round your answers to $4$ decimal places.

$\backslash$table$[[p^{-},],[$Sp$,],[$UCL$,],[$LCL$,]]$