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The text you provided appears to be a statistical problem in Armenian, involving a normal distribution. Here’s a breakdown of the problem:

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- The population mean (μ) is given as **10,000**.
- The standard deviation (σ) is given as **2**.
- The task is likely to find some probability involving a normal distribution.
- A cumulative probability value of **0.9544** is mentioned, which is close to the cumulative distribution function (CDF) value associated with approximately **2 standard deviations** away from the mean in a normal distribution (68-95-99.7 rule).

The problem seems to ask for the range within which a certain percentage of the population lies.

### To solve this:

1. **The given mean (μ)**: 10,000
2. **The standard deviation (σ)**: 2
3. **The cumulative probability (CDF)**: 0.9544, which corresponds to roughly ±2 standard deviations from the mean.

Using the fact that 0.9544 represents the area under the curve for approximately ±2σ, we can calculate:

- **Lower bound** = μ - 2σ = 10,000 - 2(2) = **9,996**
- **Upper bound** = μ + 2σ = 10,000 + 2(2) = **10,004**

Thus, approximately **95.44%** of the population values lie between **9,996** and **10,004**.

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If you need further details or explanation, feel free to ask!

Here are five questions related to this topic:

1. What is the general formula for the normal distribution?
2. How do you calculate probabilities from a standard normal distribution table?
3. What does the empirical rule (68-95-99.7) mean in the context of a normal distribution?
4. How do we interpret cumulative distribution function (CDF) values in statistics?
5. What other methods can be used to approximate probabilities in non-normal distributions?

**Tip**: When solving problems with normal distributions, it's helpful to memorize key cumulative percentages, such as 68.27%, 95.44%, and 99.73% for ±1σ, ±2σ, and ±3σ, respectively.

The population mean is given as 10,000 with a standard deviation of 2. The task is to find the probability or the range within which 95.44% of the population values lie.

This problem involves calculating the range within which 95.44% of population values lie, given a mean of 10,000 and a standard deviation of 2. Using the properties of the normal distribution, we determine the lower and upper bounds for the values.

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