Question

a police officer randomly selected 587 police records of larceny thefts. the accompanying data represent the number of offenses for various types of larceny thefts.
type of larceny theft

• pocket - picking
• purse snatching
• shoplifting
• from motor vehicles
• motor vehicle accessories
• bicycles
• from buildings
• from coin - operated machines

number of offenses

• 3
• 146
• 229
• 66
• 39
• 30
• 102
• 4

a. construct a probability model for type of larceny theft.
type of larceny theft

• pocket - picking
• purse snatching
• shoplifting
• from motor vehicles
• motor vehicle accessories
• bicycles
• from buildings
• from coin - operated machines

probability

• 3/587 = 0.0051
• 146/587 = 0.2487
• 229/587 = 0.3901
• 66/587 = 0.1124
• 39/587 = 0.0664
• 30/587 = 0.0511
• 102/587 = 0.1738
• 4/587 = 0.0068

b. are pocket - picking larcenies unusual?
c. are larcenies from buildings unusual?

Explanation:

Step1: Recall probability - model concept

A probability model for the type of larceny theft lists the types of larceny thefts and their corresponding probabilities. The sum of all probabilities in a probability - model must equal 1.

Step2: Analyze part (a)

The probability model is constructed by dividing the number of offenses for each type of larceny theft by the total number of larceny thefts (587). For example, for pocket - picking, the probability is $\frac{2}{587}\approx0.0034$; for purse snatching, it is $\frac{3}{587}\approx0.0051$; for shoplifting, $\frac{146}{587}\approx0.2487$; for from motor vehicles, $\frac{229}{587}\approx0.3901$; for motor vehicle accessories, $\frac{60}{587}\approx0.1022$; for bicycles, $\frac{30}{587}\approx0.0511$; for from buildings, $\frac{102}{587}\approx0.1738$; for from coin - operated machines, $\frac{4}{587}\approx0.0068$.

Step3: Analyze part (b)

To determine if pocket - picking larcenies are unusual, we use the range - rule - of - thumb for significant events. Unusual events have a probability of 0.05 or less. Since the probability of pocket - picking larcenies ($\frac{2}{587}\approx0.0034$) is less than 0.05, pocket - picking larcenies are unusual.

Step4: Analyze part (c)

For larcenies from buildings, the probability is $\frac{102}{587}\approx0.1738$. Since $0.1738> 0.05$, larcenies from buildings are not unusual.

Answer:

a. Probability model:

Type of Larceny Theft	Probability
Purse snatching	$\frac{3}{587}\approx0.0051$
Shoplifting	$\frac{146}{587}\approx0.2487$
From motor vehicles	$\frac{229}{587}\approx0.3901$
Motor vehicle accessories	$\frac{60}{587}\approx0.1022$
Bicycles	$\frac{30}{587}\approx0.0511$
From buildings	$\frac{102}{587}\approx0.1738$
From coin - operated machines	$\frac{4}{587}\approx0.0068$

b. Yes, pocket - picking larcenies are unusual.
c. No, larcenies from buildings are not unusual.