Question
There are 600 employees at Dani's office. She asks a random sample of employees how they get to the office. The results show that 7 employees in the sample drive to the office and 23 take public transportation
Approximately what fraction of all employees can dani expect to drive to the office?
how can dani estimate the total number of employees who drive to the office?
Approximately what fraction of all employees can dani expect to drive to the office?
how can dani estimate the total number of employees who drive to the office?
Answers
GPT-4o mini
To estimate the fraction of all employees at Dani's office that drive to the office, you can first determine the total number of employees in the sample and then calculate the proportion of those employees who drive.
1. **Total sample size**:
- Employees who drive: 7
- Employees who take public transportation: 23
- Total sample size = 7 + 23 = 30
2. **Fraction of employees who drive in the sample**:
\[
\text{Fraction driving} = \frac{\text{Number of employees who drive}}{\text{Total employees in sample}} = \frac{7}{30}
\]
3. **Approximate fraction for the entire office**:
Assuming the sample is representative of the entire office of 600 employees, we can keep this fraction the same:
- Estimated fraction of all employees who drive = \(\frac{7}{30}\)
4. **Estimate the total number of employees who drive**:
To find the estimated total number of employees who drive, multiply the fraction by the total number of employees:
\[
\text{Estimated number of drivers} = \text{Total number of employees} \times \text{Fraction driving}
\]
\[
\text{Estimated number of drivers} = 600 \times \frac{7}{30}
\]
5. **Calculating**:
\[
\text{Estimated number of drivers} = 600 \times \frac{7}{30} = 600 \times 0.2333 \approx 140
\]
Thus, Dani can expect approximately \( \frac{7}{30} \) of the employees to drive to the office, and she can estimate that about 140 employees drive to the office.
1. **Total sample size**:
- Employees who drive: 7
- Employees who take public transportation: 23
- Total sample size = 7 + 23 = 30
2. **Fraction of employees who drive in the sample**:
\[
\text{Fraction driving} = \frac{\text{Number of employees who drive}}{\text{Total employees in sample}} = \frac{7}{30}
\]
3. **Approximate fraction for the entire office**:
Assuming the sample is representative of the entire office of 600 employees, we can keep this fraction the same:
- Estimated fraction of all employees who drive = \(\frac{7}{30}\)
4. **Estimate the total number of employees who drive**:
To find the estimated total number of employees who drive, multiply the fraction by the total number of employees:
\[
\text{Estimated number of drivers} = \text{Total number of employees} \times \text{Fraction driving}
\]
\[
\text{Estimated number of drivers} = 600 \times \frac{7}{30}
\]
5. **Calculating**:
\[
\text{Estimated number of drivers} = 600 \times \frac{7}{30} = 600 \times 0.2333 \approx 140
\]
Thus, Dani can expect approximately \( \frac{7}{30} \) of the employees to drive to the office, and she can estimate that about 140 employees drive to the office.