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?

Answer 1

To estimate the fraction of all employees that can be expected to drive to the office, we start by calculating the fraction of employees in the sample who drive.

From the information provided:
- Number of employees who drive in the sample = 7
- Number of employees who take public transportation in the sample = 23
- Total number of employees in the sample = 7 + 23 = 30

Now, we calculate the fraction of the sample that drives:

\[
\text{Fraction of sample driving} = \frac{\text{Number of employees who drive}}{\text{Total number of employees in sample}} = \frac{7}{30}
\]

Next, we can use this fraction to estimate the number of all employees at the office who drive:

\[
\text{Expected number of employees driving} = \text{Total employees} \times \text{Fraction driving} = 600 \times \frac{7}{30}
\]

Calculating this gives:

\[
\text{Expected number of employees driving} = 600 \times \frac{7}{30} = 600 \times 0.2333 \approx 140
\]

Thus, the expected fraction of all employees who drive to the office is:

\[
\text{Expected fraction of all employees driving} = \frac{140}{600} = \frac{7}{30}
\]

Therefore, Dani can expect approximately **\(\frac{7}{30}\)** of all employees to drive to the office.