Below is a graph of a normal distribution with mean μ=-1 and standard deviation G=4. The shaded region represents the probability of obtaining a value from this distribution that is between -9 and 1. 0.44 0.3- 0.2- 01 Shade the corresponding region under the standard normal curve below. 0.4. 0.24 0.1-

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### Understanding Normal Distribution: An Educational Perspective

**Normal Distribution**

Below is a graph of a [normal distribution](https://en.wikipedia.org/wiki/Normal_distribution) with mean \( \mu = -1 \) and standard deviation \( \sigma = 4 \). The shaded region represents the probability of obtaining a value from this distribution that is between \( -9 \) and \( 1 \).

**Graph 1: Normal Distribution**

- **X-Axis:** Represents the range of values in the distribution, from \( -9 \) to \( +9 \).
- **Y-Axis:** Represents the probability density of the distribution, ranging from 0 to 0.4.
- **Shaded Region:** The area under the curve between \( -9 \) and \( 1 \). This indicates the probability of the values falling within this range in the given normal distribution.

![First Graph](#)

**Task: Shade the Standard Normal Curve**

Shade the corresponding region under the [standard normal](https://en.wikipedia.org/wiki/Standard_normal_table) curve below.

**Graph 2: Standard Normal Distribution**

- **X-Axis:** Represents the range of values in the standard normal distribution, from \( -9 \) to \( +9 \).
- **Y-Axis:** Represents the probability density of the distribution, ranging from 0 to 0.4.
- **Objective:** Identify and shade the region of the standard normal curve that corresponds to the same probability region as indicated in Graph 1.

**Interactive Tools:**

- **Eraser Tool:** To erase any incorrectly shaded regions.
- **Draw Tool:** To shade areas on the graph.
- **Selection Tool:** To select and adjust the shaded areas.
- **Reset Button:** To clear all work and start over.

Graphing these distributions helps to visualize and understand how probabilities are distributed and compared in different normal distributions.
Transcribed Image Text:### Understanding Normal Distribution: An Educational Perspective **Normal Distribution** Below is a graph of a [normal distribution](https://en.wikipedia.org/wiki/Normal_distribution) with mean \( \mu = -1 \) and standard deviation \( \sigma = 4 \). The shaded region represents the probability of obtaining a value from this distribution that is between \( -9 \) and \( 1 \). **Graph 1: Normal Distribution** - **X-Axis:** Represents the range of values in the distribution, from \( -9 \) to \( +9 \). - **Y-Axis:** Represents the probability density of the distribution, ranging from 0 to 0.4. - **Shaded Region:** The area under the curve between \( -9 \) and \( 1 \). This indicates the probability of the values falling within this range in the given normal distribution. ![First Graph](#) **Task: Shade the Standard Normal Curve** Shade the corresponding region under the [standard normal](https://en.wikipedia.org/wiki/Standard_normal_table) curve below. **Graph 2: Standard Normal Distribution** - **X-Axis:** Represents the range of values in the standard normal distribution, from \( -9 \) to \( +9 \). - **Y-Axis:** Represents the probability density of the distribution, ranging from 0 to 0.4. - **Objective:** Identify and shade the region of the standard normal curve that corresponds to the same probability region as indicated in Graph 1. **Interactive Tools:** - **Eraser Tool:** To erase any incorrectly shaded regions. - **Draw Tool:** To shade areas on the graph. - **Selection Tool:** To select and adjust the shaded areas. - **Reset Button:** To clear all work and start over. Graphing these distributions helps to visualize and understand how probabilities are distributed and compared in different normal distributions.
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