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The problem is about a statistical analysis of income (in ten thousand units) after promoting exports in a certain area, using sample statistics to make inferences.

Let's break down the problem:

- **Given:**
  - The sample mean of the post-promotion income \( \bar{X} = 2.1 \).
  - The sample variance \( s^2 = 0.01 \).
  - The normal distribution of the post-promotion income \( X \) in the area follows \( N(1.8, 0.12) \).

- **Tasks:**
  1. Determine if the statement \( P(Y > 2) \) (where \( Y \) is from \( N(\bar{X}, s^2) \)) is true for given probabilities.

- **Assumptions:**
  - \( Y \) is normally distributed as \( N(\bar{X}, s^2) \), so \( Y \sim N(2.1, 0.01) \).
  - The value \( Z \) follows the distribution \( N(\mu, \sigma^2) \).

Let's solve it:

### Step-by-Step Solution

1. **Calculate the probability \( P(Y > 2) \):**

   Given that \( Y \sim N(2.1, 0.01) \), we need to find the probability that \( Y \) exceeds 2.

   The Z-score formula is:
   \[
   Z = \frac{Y - \mu}{\sigma}
   \]

   Here, \( \mu = 2.1 \) and \( \sigma = \sqrt{0.01} = 0.1 \). 

   Calculate the Z-score for \( Y = 2 \):
   \[
   Z = \frac{2 - 2.1}{0.1} = \frac{-0.1}{0.1} = -1
   \]

2. **Find the corresponding probability:**

   Using the Z-score table or standard normal distribution table:

   \[
   P(Z > -1) = 1 - P(Z \leq -1)
   \]
   The value for \( P(Z \leq -1) \approx 0.1587 \).

   Thus,
   \[
   P(Z > -1) = 1 - 0.1587 = 0.8413
   \]

3. **Conclusion:**

   The probability \( P(Y > 2) \approx 0.8413 \).

This value of 0.8413 indicates that the correct answer should be:
- **(D)** \( P(Y > 2) < 0.8 \) is false because \( P(Y > 2) = 0.8413 \).
- Therefore, **(A)** \( P(X > 2) = 0.2 \) is also false since \( P(Y > 2) = 0.8413 \).
- **(B)** \( P(X > 2) < 0.5 \) is false because \( P(Y > 2) > 0.5 \).
- **(C)** \( P(Y > 2) < 0.8 \) is true because \( P(Y > 2) = 0.8413 \).

### Final Answer

The correct choice is:

\[ \text{None of the choices accurately reflect } P(Y > 2) = 0.8413 \text{ but if choices were provided correctly, choose based on calculations.} \]

**Questions you can ask:**
1. How to interpret normal distribution in practical scenarios?
2. What are the applications of Z-scores in statistics?
3. How to use a Z-score table to find probabilities?
4. What assumptions are made in normal distribution?
5. How to calculate probabilities for different distributions?

**Tip:** Always verify your results with standard statistical tables or tools to ensure accuracy in probability calculations.

Explore a detailed solution to a statistical problem involving the calculation of probabilities using normal distribution. This problem focuses on finding the probability that a variable exceeds a given value, utilizing the concepts of sample mean, variance, and Z-score. Suitable for advanced high school students.

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