# Step-by-Step Solution with Tables and Explanations Let's break down the problem and solve each part using **realistic sample data** for 240 applicants. --- ## 1. **Grouped Frequency Distribution Table for Monthly Income** ### **Given:** - Monthly income range: ₹20,000 to ₹1,50,000 - Class interval width: ₹20,000 ### **Class Intervals:** 1. ₹20,000 – ₹39,999 2. ₹40,000 – ₹59,999 3. ₹60,000 – ₹79,999 4. ₹80,000 – ₹99,999 5. ₹1,00,000 – ₹1,19,999 6. ₹1,20,000 – ₹1,39,999 7. ₹1,40,000 – ₹1,50,000 ### **Sample Frequency Data:** Let's assume the following distribution of 240 applicants: | Income Interval (₹) | Frequency | Cumulative Frequency | Relative Frequency | Percentage | |--------------------------|-----------|---------------------|-------------------|------------| | 20,000 – 39,999 | 20 | 20 | .083 | 8.3% | | 40,000 – 59,999 | 36 | 56 | .150 | 15.% | | 60,000 – 79,999 | 44 | 100 | .183 | 18.3% | | 80,000 – 99,999 | 54 | 154 | .225 | 22.5% | | 1,00,000 – 1,19,999 | 42 | 196 | .175 | 17.5% | | 1,20,000 – 1,39,999 | 28 | 224 | .117 | 11.7% | | 1,40,000 – 1,50,000 | 16 | 240 | .067 | 6.7% | | **Total** | **240** | | **1.00** | **100%** | --- ## 2. **Grouped Frequency Distribution Table for Credit Scores** ### **Given:** - Credit score range: 300 to 900 - Class interval width: 100 ### **Class Intervals:** 1. 300 – 399 2. 400 – 499 3. 500 – 599 4. 600 – 699 5. 700 – 799 6. 800 – 900 ### **Sample Frequency Data:** | Credit Score Interval | Frequency | Cumulative Frequency | Relative Frequency | Percentage | |----------------------|-----------|---------------------|-------------------|------------| | 300 – 399 | 12 | 12 | .05 | 5.% | | 400 – 499 | 24 | 36 | .10 | 10.% | | 500 – 599 | 36 | 72 | .15 | 15.% | | 600 – 699 | 60 | 132 | .25 | 25.% | | 700 – 799 | 68 | 200 | .28 | 28.3% | | 800 – 900 | 40 | 240 | .17 | 16.7% | | **Total** | **240** | | **1.00** | **100%** | --- ## 3. **Two-Way Contingency Table: Income Intervals vs Loan Status** ### **Sample Table:** | Income Interval (₹) | Approved | Rejected | Total | |-------------------------|----------|----------|-------| | 20,000 – 39,999 | 10 | 10 | 20 | | 40,000 – 59,999 | 26 | 10 | 36 | | 60,000 – 79,999 | 36 | 8 | 44 | | 80,000 – 99,999 | 48 | 6 | 54 | | 1,00,000 – 1,19,999 | 38 | 4 | 42 | | 1,20,000 – 1,39,999 | 24 | 4 | 28 | | 1,40,000 – 1,50,000 | 12 | 4 | 16 | | **Total** | **194** | **46** | **240** | --- ## 4. **Summary Table: Average Loan Amount Requested Within Each Income Class** | Income Interval (₹) | Average Loan Amount Requested (₹) | |-------------------------|-----------------------------------| | 20,000 – 39,999 | 1,00,000 | | 40,000 – 59,999 | 1,80,000 | | 60,000 – 79,999 | 2,50,000 | | 80,000 – 99,999 | 3,20,000 | | 1,00,000 – 1,19,999 | 4,00,000 | | 1,20,000 – 1,39,999 | 5,00,000 | | 1,40,000 – 1,50,000 | 6,00,000 | --- ## 5. **Probability Calculation** ### **Question:** Probability that a randomly selected applicant has income **above ₹80,000** and the loan is **approved**. - Income above ₹80,000: includes classes 4 to 7 (from the income table) - Approved in these classes: 48 + 38 + 24 + 12 = **122** - Total applicants = **240** ### **Probability Calculation:** \[ P(\text{Income} > ₹80{,}000 \text{ and Approved}) = \frac{122}{240} = .508 \] **Probability = .508 or 50.8%** --- # **Summary Table of Results** | Task | Table/Value | |------|-------------| | Grouped Frequency Table (Income) | See Section 1 | | Grouped Frequency Table (Credit Score) | See Section 2 | | Two-Way Contingency Table | See Section 3 | | Avg. Loan per Income Class | See Section 4 | | Probability (Income > ₹80,000 & Approved) | .508 or 50.8% | --- > **All tables above are structured with clear headings and totals for easy reference.** > **If you need the data in Excel or any specific format, let me know!**