1. **State the problem:** We are given a pie chart representing 120 gym members' daily exercise amounts. The chart sections are: - 162° for "< 30 minutes" - 108° for "30 - 60 minutes" - The remaining angle for "> 60 minutes" We need to find: a) How many members exercise at least 30 minutes each day? b) Why a newspaper's claim that most people do this might be incorrect. 2. **Calculate total degrees of a circle:** The total degrees in a pie chart are always $360^\circ$. 3. **Find the angle of the "> 60 minutes" sector:** $$360^\circ - 162^\circ - 108^\circ = 90^\circ$$ 4. **Find the fraction of members for each exercise category:** - For "< 30 minutes": $\frac{162}{360} = \frac{9}{20}$ - For "30 - 60 minutes": $\frac{108}{360} = \frac{3}{10}$ - For "> 60 minutes": $\frac{90}{360} = \frac{1}{4}$ 5. **Calculate the number of members for each category:** - "< 30 minutes": $120 \times \frac{9}{20} = 54$ - "30 - 60 minutes": $120 \times \frac{3}{10} = 36$ - "> 60 minutes": $120 \times \frac{1}{4} = 30$ 6. **Answer part (a):** Members doing at least 30 minutes means those doing "30 - 60 minutes" or "> 60 minutes": $$36 + 30 = 66$$ So, \textbf{66 members say they exercise at least 30 minutes daily}. 7. **Answer part (b):** The newspaper's claim that most people in the country exercise at least 30 minutes daily is incorrect because: - The data is only from gym members, not the whole country. - This group may be more active than the average population. - It’s a specific sample, not representative of general population habits. Thus, generalizing these results to the entire country is misleading.