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?

About how many employees at the company can Dani expect to the office?

Answer 1

To estimate the fraction of all employees who drive to the office based on Dani's sample, we can use the results from the sample.

1. **Fraction of employees who drive:**
In the sample, 7 employees drive and 23 take public transportation. Thus, the total number of employees in the sample is:
\[
7 + 23 = 30
\]
The fraction of employees who drive is:
\[
\text{Fraction who drive} = \frac{\text{Number who drive}}{\text{Total sample size}} = \frac{7}{30}
\]

2. **Estimate total number of employees who drive:**
To estimate the total number of employees at Dani's office who drive to the office, we can multiply the fraction of employees who drive by the total number of employees:
\[
\text{Estimated number who drive} = \text{Total employees} \times \text{Fraction who drive} = 600 \times \frac{7}{30}
\]
Calculating this:
\[
600 \times \frac{7}{30} = 600 \div 30 \times 7 = 20 \times 7 = 140
\]

3. **Total number of employees who take public transportation:**
Since 140 employees are estimated to drive, we can find the estimated number of employees who take public transportation by subtracting the number who drive from the total:
\[
\text{Estimated number who take public transportation} = 600 - 140 = 460
\]

**Summary of Estimates:**
- Fraction of all employees expected to drive to the office: \(\frac{7}{30}\)
- Estimated total number of employees who drive to the office: **140**
- Estimated total number of employees who take public transportation: **460**