To estimate the total number of students in the school who prefer orange sherbet, we can use the proportion of students who prefer orange sherbet in the sample and apply it to the total number of students in the school.
In Pablo's survey, the number of students who preferred orange sherbet is 10 out of 130 surveyed students.
Now, we calculate the proportion of students who prefer orange sherbet:
\[ \text{Proportion for orange sherbet} = \frac{10}{130} \]
Next, we find the equivalent number of students in the total population (528 students) who would prefer orange sherbet:
\[ \text{Estimated number of students for orange sherbet} = \text{Total students} \times \text{Proportion for orange sherbet} \]
Substituting the values:
\[ \text{Estimated number of students for orange sherbet} = 528 \times \frac{10}{130} \]
Calculating this gives:
\[ = 528 \times \frac{10}{130} = 528 \times \frac{1}{13} \approx 40.615 \approx 41 \]
Thus, approximately 41 students in the school prefer orange sherbet.
The answer is 41.
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