Problem $13-11$

The state and local police departments are trying to analyze crime rates so they can shift their patrols from decreasing$-$rate areas to areas where rates are increasing. The city and county have been geographically segmented into areas containing $5,750$ residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among othefre reasons. Every month, because of this, the police are contacting by phone a random sample of $1,150$ of the $5,750$ residences for data on crime. $($Respondents are guaranteed anonymity.$)$ Here are the data collected for the past $12$ months for one area:

$\backslash$begin$\{$tabular$\}\{$lccc$\}$

& CRIME & SAMPLE & CRIME $\backslash \backslash$

MONTH & INCIDENCE & SIZE & RATE $\backslash \backslash$

January & $8$ & $1,150$ & $0\mathrm{.}007\backslash \backslash$

February & $10$ & $1,150$ & $0\mathrm{.}009\backslash \backslash$

March & $8$ & $1,150$ & $0\mathrm{.}007\backslash \backslash$

April & $8$ & $1,150$ & $0\mathrm{.}007\backslash \backslash$

May & $8$ & $1,150$ & $0\mathrm{.}007\backslash \backslash$

June & $10$ & $1,150$ & $0\mathrm{.}009\backslash \backslash$

July & $8$ & $1,150$ & $0\mathrm{.}007\backslash \backslash$

August & $11$ & $1,150$ & $0\mathrm{.}010\backslash \backslash$

September & $9$ & $1,150$ & $0\mathrm{.}008\backslash \backslash$

October & $12$ & $1,150$ & $0\mathrm{.}010\backslash \backslash$

November & $11$ & $1,150$ & $0\mathrm{.}010\backslash \backslash$

December & $9$ & $1,150$ & $0\mathrm{.}008\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$.$

Determine the $\backslash (\backslash$bar$\{$P$\},$ S$\_\{$p$\},\backslash$cup C L $\backslash )$ and LCL for a $\backslash ($ p $\backslash )-$chart of $95$ percent confidence $($at $\backslash ($ Z$=\backslash )1\mathrm{.}96).($Round your answers to $5$ decimal places.$)$