This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the mean score. The raw scores of 20 students are: 38, 28, 70, 43, 39, 20, 64, 66, 12, 46, 52, 53, 20, 34, 48, 69, 18, 20, 64, 34. The number of students is n = 20. The sum of the scores is: x = 38+28+70+43+39+20+64+66+12+46+52+53+20+34+48+69+18+20+64+34 = 838 The mean score (x) is: x = ( x)/(n) = (838)/(20) = 41.9 a) The mean score of the student's mark is 41.9. Step 2: Determine the number of students who passed the examination. The pass mark is 40%. Students who scored 40 or above passed. The scores 40 are: 70, 43, 64, 66, 46, 52, 53, 48, 69, 64. There are 10 students who passed. b) The number of students who passed the examination is 10. Step 3: Calculate the percentage of students who failed the examination. Students who scored below 40 failed. The scores < 40 are: 38, 28, 39, 20, 12, 20, 34, 18, 20, 34. There are 10 students who failed. The percentage of students who failed is: Number of failed studentsTotal number of students × 100\% = (10)/(20) × 100\% = 50\% c) The percentage of students who failed the examination is 50\%. Step 4: Determine the number of students who scored below the mean score. The mean score is 41.9. The scores below 41.9 are: 38, 28, 39, 20, 12, 20, 34, 18, 20, 34. There are 10 students who scored below the mean score. d) The number of students who scored below the mean score is 10. Step 5: Calculate the range of the scores. First, identify the minimum and maximum scores. Minimum score = 12. Maximum score = 70. The range is the difference between the maximum and minimum scores: Range = Maximum score - Minimum score = 70 - 12 = 58 e) The range of the scores is 58. --- Question 2: a) State five roles OPEC plays in the production, refining, and marketing of petroleum in member nations. 1. Coordinating Petroleum Policies: OPEC coordinates and unifies the petroleum policies of its member countries to secure fair and stable prices for petroleum producers. 2. Stabilizing Oil Markets: It works to stabilize international oil markets to ensure an efficient, economic, and regular supply of petroleum to consuming nations. 3. Ensuring Fair Returns: OPEC aims to ensure a steady income for oil-producing countries and a fair return on capital for those investing in the petroleum industry. 4. Influencing Production Levels: Through collective agreements on production quotas, OPEC influences global oil supply and, consequently, international oil prices. 5. Promoting Sustainable Development: It promotes sustainable development and environmental protection in the oil industry within its member states. b) Enumerate five problems facing the organization. 1. Internal Disagreements: Member countries often have differing economic interests and political agendas, leading to difficulties in reaching consensus on production quotas and pricing strategies. 2. Competition from Non-OPEC Producers: The rise of non-OPEC oil producers (e.g., shale oil from the US) has reduced OPEC's market share and influence. 3. Global Economic Slowdowns: Economic recessions or slowdowns in major consuming nations can significantly reduce global oil demand, putting downward pressure on prices. 4. Geopolitical Tensions: Conflicts and political instability in key member states can disrupt oil supply, create uncertainty, and strain relations within the organization. 5