To estimate how many students in the entire school prefer orange sherbet based on the survey data, we can use the proportion of surveyed students who prefer orange sherbet and apply that proportion to the total number of students in the school.
From the survey:
- Total number of surveyed students: 130
- Number of students who prefer orange sherbet: 10
First, calculate the proportion of students who prefer orange sherbet: \[ \text{Proportion for orange sherbet} = \frac{\text{Number of students who prefer orange sherbet}}{\text{Total surveyed}} = \frac{10}{130} \]
To find out how many students in the entire school (528 students) prefer orange sherbet, we use this proportion: \[ \text{Estimated number of students in school preferring orange sherbet} = \text{Proportion for orange sherbet} \times \text{Total number of students in school} \] \[ \text{Estimated number} = \left(\frac{10}{130}\right) \times 528 \] \[ \text{Estimated number} = \frac{10 \times 528}{130} \approx \frac{5280}{130} \approx 40.615 \]
Rounding this to the nearest whole number gives approximately 41.
Therefore, the answer is 41.