For the above normal distribution, where does approximately 99.7% of the scores fall within?

Ciccarelli: Psychology_5 (5th Edition)
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Chapter1: The Science Of Psychology
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For the above normal distribution, where does approximately 99.7% of the scores fall within? 

### Understanding Normal Distribution

The image above depicts a **normal distribution curve**, which is a common continuous probability distribution in statistics. This curve is bell-shaped and symmetric around the mean.

#### Key Features of the Normal Distribution:

1. **Mean (μ)**:
   - The mean (average) of the distribution is denoted by μ.
   - In this diagram, **μ = 3**.
   - The mean is the peak or the highest point of the curve, indicating the most probable value.

2. **Standard Deviation (σ)**:
   - The standard deviation measures the spread of the distribution.
   - Here, **σ = 1**.
   - A smaller standard deviation results in a steeper curve, while a larger one would flatten it.

#### Curve Characteristics:

- The curve is symmetric, meaning the left side is a mirror image of the right.
- As you move away from the mean, the probability decreases, indicating lower likelihoods for values further from the mean.
- The tails of the curve approach, but never touch, the horizontal axis.

This graph is vital in understanding how values are distributed in a given set of data, especially in fields like psychology, business, and natural sciences where data tends to form a normal distribution.
Transcribed Image Text:### Understanding Normal Distribution The image above depicts a **normal distribution curve**, which is a common continuous probability distribution in statistics. This curve is bell-shaped and symmetric around the mean. #### Key Features of the Normal Distribution: 1. **Mean (μ)**: - The mean (average) of the distribution is denoted by μ. - In this diagram, **μ = 3**. - The mean is the peak or the highest point of the curve, indicating the most probable value. 2. **Standard Deviation (σ)**: - The standard deviation measures the spread of the distribution. - Here, **σ = 1**. - A smaller standard deviation results in a steeper curve, while a larger one would flatten it. #### Curve Characteristics: - The curve is symmetric, meaning the left side is a mirror image of the right. - As you move away from the mean, the probability decreases, indicating lower likelihoods for values further from the mean. - The tails of the curve approach, but never touch, the horizontal axis. This graph is vital in understanding how values are distributed in a given set of data, especially in fields like psychology, business, and natural sciences where data tends to form a normal distribution.
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