Questions: A police officer randomly selected 593 police records of larceny thefts. The accompanying data represent the number of offenses for various types of larceny thefts. (a) Construct a probability model for type of larceny theft. (b) Are purse-snatching larcenies unusual? (c) Are larcenies from buildings unusual? Complete the table below. 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.)

Solution Steps

The probability model for the types of larceny thefts is calculated by dividing the number of offenses for each type by the total number of records (593). The probabilities are as follows:

\[ \begin{align_} \text{Pocket picking} & : 0.017 \\ \text{Purse snatching} & : 0.059 \\ \text{Shoplifting} & : 0.253 \\ \text{From motor vehicles} & : 0.337 \\ \text{Motor vehicle accessories} & : 0.084 \\ \text{Bicycles} & : 0.051 \\ \text{From buildings} & : 0.169 \\ \text{From coin-operated machines} & : 0.030 \\ \end{align_} \]

To determine if purse-snatching larcenies are unusual, we examine the probability:

\[ P(\text{Purse snatching}) = 0.059 \]

Since this probability is relatively low, purse-snatching larcenies can be considered unusual.

Next, we evaluate the probability of larcenies from buildings:

\[ P(\text{From buildings}) = 0.169 \]

This probability is higher than that of purse-snatching, indicating that larcenies from buildings are not considered unusual.

The statistical properties of the distribution are calculated as follows:

• Mean (\(\mu\)): \[ \mu = 10 \times 0.017 + 35 \times 0.059 + 150 \times 0.253 + 200 \times 0.337 + 50 \times 0.084 + 30 \times 0.051 + 100 \times 0.169 + 18 \times 0.030 = 130.774 \]

• Variance (\(\sigma^2\)): \[ \sigma^2 = 4106.765 \]

• Standard Deviation (\(\sigma\)): \[ \sigma = \sqrt{4106.765} \approx 64.084 \]

Final Answer