Problem $10-28($Algo$)$

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of

crimes. The citizens argued that this equal protection should be interpreted as indicating that high$-$crime areas should have more

police protection than low$-$crime areas. Therefore, police patrols and other methods for preventing crime $($such as street lighting or

cleaning up abandoned areas and buildings$)$ should be used proportionately to crime occurrence.

The city has been broken down into $20$ geographic areas, each containing $5,000$ 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 other reasons. Every month, because of this, the police are contacting by phone

a random sample of $1,000$ of the $5,000$ residences for data on crime. $($Respondents are guaranteed anonymity.$)$ The $1,000$ sampled

from each area showed the following incidence of crime during the past month:

a$.$ Determine $\frac{?}{\text{b}\text{a}\text{r}}(P),S_p,$UCL and $LCL$ for a $p$ chart of $95$ percent confidence $($at $Z=1\mathrm{.}96).$

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

b$.$ What can you say about the process?

Process is in statistical control.

Process is out of statistical control.