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The question asks us to find the lowest income of the richest 250 people from a group of 10,000, where the income is normally distributed with a mean of Rs 750 and a standard deviation of Rs 50.

### Solution:

1. **Normal Distribution Properties**:
   Since the distribution is normal, we can use the Z-score formula to determine the income of the richest 250 people. The Z-score corresponding to the richest 250 out of 10,000 can be found using the cumulative distribution function (CDF).

2. **Proportion of Richest People**:
   The richest 250 people represent the top 250/10,000 = 0.025 or 2.5% of the population.

   We need to find the Z-score corresponding to the 97.5th percentile (since 100% - 2.5% = 97.5%).

3. **Finding Z-score**:
   From standard normal distribution tables or using statistical tools, the Z-score for the 97.5th percentile is approximately **1.96**.

4. **Z-score Formula**:
   The Z-score formula is given by:
   \[
   Z = \frac{X - \mu}{\sigma}
   \]
   where:
   - \( Z \) is the Z-score,
   - \( X \) is the value we are solving for (income),
   - \( \mu \) is the mean income (Rs 750),
   - \( \sigma \) is the standard deviation (Rs 50).

   Rearranging the formula to solve for \( X \):
   \[
   X = Z \cdot \sigma + \mu
   \]
   Substituting the values:
   \[
   X = 1.96 \cdot 50 + 750
   \]
   \[
   X = 98 + 750 = 848
   \]

Thus, the lowest income of the richest 250 people is approximately **Rs 848**.

Would you like further details or have any questions?

### Related Questions:
1. How do you calculate Z-scores for a normal distribution?
2. What is the cumulative distribution function (CDF) and how is it used?
3. How do changes in mean and standard deviation affect the normal distribution?
4. What is the relationship between percentiles and Z-scores in a normal distribution?
5. How can the normal distribution be applied in other real-world scenarios?

### Tip:
When solving problems related to normal distributions, always identify the percentile you're dealing with and use Z-tables or calculators to find the corresponding Z-score.

The income of a group of 10,000 persons is found to be normally distributed with mean equal to Rs 750 with a standard deviation equal to Rs 50. Find the lowest income of the richest 250 people.

Learn how to solve a normal distribution problem to find the lowest income of the richest 250 people from a group of 10,000, where the mean income is Rs 750 and the standard deviation is Rs 50. This problem covers concepts like Z-scores, percentiles, and the normal distribution formula. Suitable for students in Grades 10-12.

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