Question

a police officer randomly selected 552 police records of larceny thefts. the accompanying data represent the number of offenses for various types of larceny (a) construct a probability model for type of larceny theft. (b) are purse - snatching larcenies unusual? (c) are motor vehicle accessory larcenies unusual? click the icon to view the table. type of larceny theft probability pocket picking purse snatching shoplifting from motor vehicles motor vehicle accessories bicycles from buildings from coin - operated machines (round to three decimal places as needed.)

Explanation:

Step1: Recall probability formula

The probability of an event $E$, $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the total number of outcomes is the total number of larceny - theft records, which is $n = 552$.

Step2: Calculate probabilities for each type

Let $n_i$ be the number of offenses of a particular type of larceny theft. Then $P_i=\frac{n_i}{552}$ for each type $i$. For example, if the number of pocket - picking offenses is $n_{pocket - picking}$, then $P_{pocket - picking}=\frac{n_{pocket - picking}}{552}$. Repeat this for all types of larceny thefts in the table.

Step3: Determine if an event is unusual

An event is considered unusual if its probability $P(E)\leq0.05$. Calculate the probabilities for purse - snatching and motor - vehicle accessory larcenies using the formula in Step 2. Then compare these probabilities with $0.05$ to determine if they are unusual.

Answer:

(a) Calculate probabilities for each type of larceny theft using $P=\frac{\text{Number of offenses of that type}}{552}$ and round to three decimal places.
(b) Calculate the probability of purse - snatching larcenies. If $P\leq0.05$, then purse - snatching larcenies are unusual; otherwise, they are not.
(c) Calculate the probability of motor - vehicle accessory larcenies. If $P\leq0.05$, then motor - vehicle accessory larcenies are unusual; otherwise, they are not. (Since the actual data from the table is not provided, the numerical values of the probabilities cannot be given).