Question

a police officer randomly selected 587 police records of larceny thefts. (a) construct a probability model for type of larceny theft. (b) are coin - operated machine 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 $n = 587$.

Step2: Calculate probabilities for each type

Let's assume the number of pocket - picking thefts is $n_1$, purse - snatching thefts is $n_2$, shoplifting thefts is $n_3$, thefts from motor vehicles is $n_4$, motor vehicle accessory thefts is $n_5$, bicycle thefts is $n_6$, thefts from buildings is $n_7$, and thefts from coin - operated machines is $n_8$. Then the probabilities are:
$P(\text{Pocket picking})=\frac{n_1}{587}$, $P(\text{Purse snatching})=\frac{n_2}{587}$, $P(\text{Shoplifting})=\frac{n_3}{587}$, $P(\text{From motor vehicles})=\frac{n_4}{587}$, $P(\text{Motor vehicle accessories})=\frac{n_5}{587}$, $P(\text{Bicycles})=\frac{n_6}{587}$, $P(\text{From buildings})=\frac{n_7}{587}$, $P(\text{From coin - operated machines})=\frac{n_8}{587}$.

Step3: Determine if an event is unusual

An event is considered unusual if its probability is less than or equal to $0.05$. Calculate the probabilities for coin - operated machine larcenies and motor vehicle accessory larcenies. If $P(\text{From coin - operated machines})\leq0.05$, then coin - operated machine larcenies are unusual. If $P(\text{Motor vehicle accessories})\leq0.05$, then motor vehicle accessory larcenies are unusual.

Since the actual number of thefts for each type is not given in the problem statement (only the table structure is shown), we cannot calculate the exact numerical values. But the general steps are as above.

Answer:

(a) Calculate probabilities for each type of larceny theft using $P(E)=\frac{\text{Number of thefts of type }E}{587}$ and round to three decimal places.
(b) Compare the probability of coin - operated machine larcenies to $0.05$. If it is $\leq0.05$, it is unusual; otherwise, it is not.
(c) Compare the probability of motor vehicle accessory larcenies to $0.05$. If it is $\leq0.05$, it is unusual; otherwise, it is not.