Problem $13-11($Algo$)$

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 $5,050$ 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 $1,010$ of the $5,050$ residences for data on crime. $($Respondents are

guaranteed anonymity.$)$ Here are the data collected for the past $12$ months for one area:

a$.$ Determine the $\frac{?}{\text{b}\text{a}\text{r}}(P),S_p,$ UCL and LCL for a $p-$chart of $95$ percent confidence $($at $Z=1\mathrm{.}96).($Round your answers to $5$ decimal places.$)$

b$.$ If the next three months show crime incidences in this area as

January $=10($out of $1,010$ sampled$)$

February $=12($out of $1,010$ sampled$)$

March $=11($out of $1,010$ sampled$)$

What comments can you make regarding the crime rate?

The process is in control.

The process is out of control.