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A company gives its employees two paid days a year to volunteer in the community. They surveyed a random sample of employees about their preferred volunteer opportunity. The table shows the results.

food pantry: 70

animal shelter: 85

park clean up: 40

Based on the results of the survey, if there are 1170 employees, how many employees can the company expect to choose to volunteer at the food pantry

3 answers

To determine how many employees can be expected to choose to volunteer at the food pantry, we first need to calculate the total number of survey responses.

From the table, we have the following number of preferences:

  • Food pantry: 70
  • Animal shelter: 85
  • Park clean up: 40

Total preferences = 70 + 85 + 40 = 195

Next, we calculate the proportion of employees who prefer the food pantry:

\[ \text{Proportion for food pantry} = \frac{\text{Number of preferences for food pantry}}{\text{Total preferences}} = \frac{70}{195} \]

Now, we will calculate this proportion:

\[ \frac{70}{195} \approx 0.358974 \]

Now, we use this proportion to find the expected number of employees who will choose to volunteer at the food pantry out of the total 1170 employees:

\[ \text{Expected number of employees for food pantry} = 0.358974 \times 1170 \approx 420 \]

Thus, the company can expect approximately 420 employees to choose to volunteer at the food pantry.

Are you sure

Let's carefully check the calculations step by step to ensure accuracy.

  1. We have the following preferences:

    • Food pantry: 70
    • Animal shelter: 85
    • Park clean-up: 40

  2. First, calculate the total number of preferences: \[ \text{Total preferences} = 70 + 85 + 40 = 195 \]

  3. Now calculate the proportion of employees who prefer the food pantry: \[ \text{Proportion for food pantry} = \frac{70}{195} \approx 0.35897435897 \]

  4. To find the expected number of employees who would choose to volunteer at the food pantry, we multiply this proportion by the total number of employees (1170): \[ \text{Expected number of employees for food pantry} = 0.35897435897 \times 1170 \approx 420 \]

Calculating that more precisely: \[ 0.35897435897 \times 1170 \approx 420.0000000031 \]

Therefore, rounding to the nearest whole number, the company can expect approximately 420 employees to choose to volunteer at the food pantry.

So yes, the original answer appears to be accurate: about 420 employees are expected to choose to volunteer at the food pantry.