Question
The CEO of a computer company surveyed a sample of employees on their job satisfaction. A random sample of 25 employees were chosen from the 135 employees in the company. The survey results are displayed in the table below.
The number of responses for very satisfied is 7, satisfied is 11, neutral is 5, and dissatisfied is 2.
Using the information in the table, predict the number of employees in the entire company who would select each of the satisfaction ratings listed. Round to the nearest whole number.
Very Satisfied:
Choose...
Satisfied:
Choose...
Neutral:
Choose...
Dissatisfied:
Choose...
The number of responses for very satisfied is 7, satisfied is 11, neutral is 5, and dissatisfied is 2.
Using the information in the table, predict the number of employees in the entire company who would select each of the satisfaction ratings listed. Round to the nearest whole number.
Very Satisfied:
Choose...
Satisfied:
Choose...
Neutral:
Choose...
Dissatisfied:
Choose...
Answers
GPT-4o mini
To predict the number of employees in the entire company who would select each satisfaction rating, we can use the proportions from the survey results and apply them to the total number of employees in the company, which is 135.
The survey results are:
- Very Satisfied: 7 responses
- Satisfied: 11 responses
- Neutral: 5 responses
- Dissatisfied: 2 responses
First, we calculate the total number of respondents:
Total responses = 7 + 11 + 5 + 2 = 25
Next, we find the proportion of each satisfaction rating:
1. Very Satisfied:
\[
\text{Proportion of Very Satisfied} = \frac{7}{25}
\]
Predicted number of Very Satisfied employees:
\[
\text{Very Satisfied} = 135 \times \frac{7}{25} = 135 \times 0.28 = 37.8 \approx 38
\]
2. Satisfied:
\[
\text{Proportion of Satisfied} = \frac{11}{25}
\]
Predicted number of Satisfied employees:
\[
\text{Satisfied} = 135 \times \frac{11}{25} = 135 \times 0.44 = 59.4 \approx 59
\]
3. Neutral:
\[
\text{Proportion of Neutral} = \frac{5}{25}
\]
Predicted number of Neutral employees:
\[
\text{Neutral} = 135 \times \frac{5}{25} = 135 \times 0.20 = 27
\]
4. Dissatisfied:
\[
\text{Proportion of Dissatisfied} = \frac{2}{25}
\]
Predicted number of Dissatisfied employees:
\[
\text{Dissatisfied} = 135 \times \frac{2}{25} = 135 \times 0.08 = 10.8 \approx 11
\]
Now, we can summarize the predictions:
- Very Satisfied: **38**
- Satisfied: **59**
- Neutral: **27**
- Dissatisfied: **11**
These are the predicted numbers of employees for each satisfaction rating in the entire company.
The survey results are:
- Very Satisfied: 7 responses
- Satisfied: 11 responses
- Neutral: 5 responses
- Dissatisfied: 2 responses
First, we calculate the total number of respondents:
Total responses = 7 + 11 + 5 + 2 = 25
Next, we find the proportion of each satisfaction rating:
1. Very Satisfied:
\[
\text{Proportion of Very Satisfied} = \frac{7}{25}
\]
Predicted number of Very Satisfied employees:
\[
\text{Very Satisfied} = 135 \times \frac{7}{25} = 135 \times 0.28 = 37.8 \approx 38
\]
2. Satisfied:
\[
\text{Proportion of Satisfied} = \frac{11}{25}
\]
Predicted number of Satisfied employees:
\[
\text{Satisfied} = 135 \times \frac{11}{25} = 135 \times 0.44 = 59.4 \approx 59
\]
3. Neutral:
\[
\text{Proportion of Neutral} = \frac{5}{25}
\]
Predicted number of Neutral employees:
\[
\text{Neutral} = 135 \times \frac{5}{25} = 135 \times 0.20 = 27
\]
4. Dissatisfied:
\[
\text{Proportion of Dissatisfied} = \frac{2}{25}
\]
Predicted number of Dissatisfied employees:
\[
\text{Dissatisfied} = 135 \times \frac{2}{25} = 135 \times 0.08 = 10.8 \approx 11
\]
Now, we can summarize the predictions:
- Very Satisfied: **38**
- Satisfied: **59**
- Neutral: **27**
- Dissatisfied: **11**
These are the predicted numbers of employees for each satisfaction rating in the entire company.