Apartment Vacancy A real estate agent conducted a survey of 200 landlords and asked how long their apartments remained vacant before a tenant was found. The results of the survey are shown in the table. The data are based on information obtained from the U.S. Census Bureau.

c. Find the probability that a randomly selected apartment is vacant for 1–4 months.

Verified step by step guidance

1. Identify the total number of landlords surveyed, which is given as 200. This will be the denominator for calculating probabilities.
2. Determine the frequency of apartments vacant for the duration of 1–4 months. This includes the categories '1–2 months' and '2–4 months'.
3. Add the frequencies for these two categories: frequency for '1–2 months' plus frequency for '2–4 months'.
4. Calculate the probability by dividing the sum of these frequencies by the total number of landlords surveyed. The formula is: \(\text{Probability} = \frac{\text{Frequency for 1–2 months} + \text{Frequency for 2–4 months}}{\text{Total frequency}}\).
5. Express the probability as a fraction or decimal to represent the likelihood that a randomly selected apartment is vacant for 1–4 months.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this context, it helps determine the chance that an apartment is vacant for a specific duration.

Frequency Distribution

A frequency distribution organizes data into categories or intervals and shows how often each occurs. Here, the table lists vacancy durations and their corresponding frequencies, which represent how many apartments fall into each vacancy time range.

Combining Intervals for Probability Calculation

When calculating probability for a range that spans multiple intervals, you sum the frequencies of all relevant categories. For example, to find the probability of vacancy lasting 1–4 months, add frequencies for 1–2 months and 2–4 months before dividing by the total.