1. **Problem Statement:** Fill in the cumulative percentages (c%) for the given distribution of shareholders by number of shares held. 2. **Given Data:** | Number of Shares Held | Percent of Shareholders (%) | Cumulative Percentage (c%) | |-----------------------|-----------------------------|----------------------------| | 0 and under 50 | 25 | ? | | 50 and under 100 | 19 | ? | | 100 and under 500 | 41 | ? | | 500 and under 1000 | 12 | ? | | 1000 and under 2000 | 3 | ? | | TOTAL | 100 | 100 | 3. **Formula and Explanation:** Cumulative percentage at each class is the sum of the percentages of all previous classes plus the current class. 4. **Calculations:** - For 0 and under 50: $$c_1 = 25$$ - For 50 and under 100: $$c_2 = 25 + 19 = 44$$ - For 100 and under 500: $$c_3 = 44 + 41 = 85$$ - For 500 and under 1000: $$c_4 = 85 + 12 = 97$$ - For 1000 and under 2000: $$c_5 = 97 + 3 = 100$$ 5. **Completed Table:** | Number of Shares Held | Percent of Shareholders (%) | Cumulative Percentage (c%) | |-----------------------|-----------------------------|----------------------------| | 0 and under 50 | 25 | 25 | | 50 and under 100 | 19 | 44 | | 100 and under 500 | 41 | 85 | | 500 and under 1000 | 12 | 97 | | 1000 and under 2000 | 3 | 100 | 6. **Answer to part b:** Percentage of shareholders holding 200 or more shares means those holding shares from 200 upwards. Since 200 is between 100 and 500, we consider cumulative percentage up to 100 under 500 which is 85%. So, percentage holding less than 200 shares is approximately 85% (since 200 is within 100-500 range, we approximate). Therefore, percentage holding 200 or more shares is $$100 - 85 = 15\%$$. But the options given are 40, 46, 54, 50. Since 15% is not an option, we interpret the question as percentage holding 200 or more shares approximately equals percentage holding 200 or more shares, which is the complement of cumulative percentage at 100 under 500 minus the portion below 200. Assuming uniform distribution in 100-500 range, shares 200 and above correspond to $$\frac{500-200}{500-100} = \frac{300}{400} = 0.75$$ of the 41% in that class. So, percentage holding 200 or more shares in that class is $$0.75 \times 41 = 30.75\%$$. Adding shareholders in higher classes (12% + 3% = 15%), total is $$30.75 + 15 = 45.75\%$$, approximately 46%. **Answer:** B. 46 7. **Answer to part c:** 20% of shareholders who own the most shares means top 20% cumulative from the top. From cumulative percentages: - 1000 and under 2000: 3% - 500 and under 1000: 12% (cumulative 15%) - 100 and under 500: 41% (cumulative 56%) Top 20% lies within 100 and under 500 and above 500 and under 1000. Since 15% cumulative from top is less than 20%, we need to go into 100 and under 500 class. Assuming uniform distribution, to reach 20%, need additional 5% from 100-500 class. Fraction needed: $$\frac{5}{41} \approx 0.122$$. Range 100 to 500 is 400 shares, so shares corresponding to top 20% start at: $$100 + 0.122 \times 400 = 100 + 48.8 = 148.8$$ shares. Closest answer choice is 155. **Answer:** B. 155