1. **State the problem:** We have 240 gym members surveyed about their daily exercise time, represented by a pie chart with angles 108° for "< 30 minutes," 162° for "> 60 minutes," and the remaining angle for "30 - 60 minutes." We want to find how many members exercise at least 30 minutes daily (i.e., those in "30 - 60 minutes" and "> 60 minutes" groups).
2. **Formula and rules:** The number of members in each category is proportional to the angle of the pie chart sector. Total angle in a circle is 360°. Number in a category = $\frac{\text{angle}}{360} \times 240$.
3. **Calculate the angle for "30 - 60 minutes":**
$$\text{angle}_{30-60} = 360^\circ - 108^\circ - 162^\circ = 90^\circ$$
4. **Calculate members exercising at least 30 minutes:**
- Members in "30 - 60 minutes":
$$240 \times \frac{90}{360} = 240 \times \frac{1}{4} = 60$$
- Members in "> 60 minutes":
$$240 \times \frac{162}{360} = 240 \times \frac{9}{20} = 108$$
- Total members exercising at least 30 minutes:
$$60 + 108 = 168$$
5. **Answer to part (a):** 168 members said they do at least 30 minutes of exercise each day.
6. **Answer to part (b):** The newspaper might be incorrect because the survey only includes gym members, who are likely more active than the general population. Therefore, the sample is biased and not representative of the whole country.
Exercise Time Abfb9D
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.