The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1800 and the standard deviation is $50. 1650 1700 1750 1800 1850 1900 1950 Distribution of Prices What is the approximate percentage of buyers who paid less than $1650? What is the approximate percentage of buyers who paid less than $1700? What is the approximate percentage of buyers who paid between $1700 and $1800? What is the approximate percentage of buyers who paid between $1750 and $1850? What is the approximate percentage of buyers who paid between $1800 and $1850? What is the approximate percentage of buyers who paid between $1650 and $1800?

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Could you answer all 6 of the questions in the picture please ? 

### Understanding Normal Distribution of Prices for HD Televisions

The following graph illustrates a normal distribution of the prices paid for a particular model of HD television. The mean price paid is $1800, with a standard deviation of $50. A normal distribution is characterized by a symmetrical bell-shaped curve where most of the data points cluster around the mean.

**Graph Description:**
- **X-axis (Horizontal):** Represents the price range for the HD television.
- **Y-axis (Vertical):** Illustrates the distribution frequency of the prices.
- **Mean (Center of distribution):** $1800
- **Standard Deviation:** $50

**Breakdown of Price Distribution:**
- The distribution spans from approximately $1650 to $1950.

### Questions and their Interpretations

1. **What is the approximate percentage of buyers who paid less than $1650?**
   - This value represents the portion of the distribution to the left of $1650. 

2. **What is the approximate percentage of buyers who paid less than $1700?**
   - This value includes all the prices below $1700.

3. **What is the approximate percentage of buyers who paid between $1700 and $1800?**
   - This value corresponds to the segment of the distribution between $1700 and $1800.

4. **What is the approximate percentage of buyers who paid between $1750 and $1850?**
   - This value accounts for the prices between $1750 and $1850.

5. **What is the approximate percentage of buyers who paid between $1800 and $1850?**
   - This value signifies the range of prices from $1800 to $1850.

6. **What is the approximate percentage of buyers who paid between $1650 and $1800?**
   - This value pertains to the distribution of prices from $1650 to $1800.

### Percentage Estimations Based on a Normal Distribution:

- **About 68%** of the data falls within one standard deviation of the mean (i.e., between $1750 and $1850).
- **About 95%** of the data lies within two standard deviations of the mean (i.e., between $1700 and $1900).
- **Approximately 99.7%** falls within three standard deviations of the mean (i.e., between $1650 and $1950).

Using the properties of the normal
Transcribed Image Text:### Understanding Normal Distribution of Prices for HD Televisions The following graph illustrates a normal distribution of the prices paid for a particular model of HD television. The mean price paid is $1800, with a standard deviation of $50. A normal distribution is characterized by a symmetrical bell-shaped curve where most of the data points cluster around the mean. **Graph Description:** - **X-axis (Horizontal):** Represents the price range for the HD television. - **Y-axis (Vertical):** Illustrates the distribution frequency of the prices. - **Mean (Center of distribution):** $1800 - **Standard Deviation:** $50 **Breakdown of Price Distribution:** - The distribution spans from approximately $1650 to $1950. ### Questions and their Interpretations 1. **What is the approximate percentage of buyers who paid less than $1650?** - This value represents the portion of the distribution to the left of $1650. 2. **What is the approximate percentage of buyers who paid less than $1700?** - This value includes all the prices below $1700. 3. **What is the approximate percentage of buyers who paid between $1700 and $1800?** - This value corresponds to the segment of the distribution between $1700 and $1800. 4. **What is the approximate percentage of buyers who paid between $1750 and $1850?** - This value accounts for the prices between $1750 and $1850. 5. **What is the approximate percentage of buyers who paid between $1800 and $1850?** - This value signifies the range of prices from $1800 to $1850. 6. **What is the approximate percentage of buyers who paid between $1650 and $1800?** - This value pertains to the distribution of prices from $1650 to $1800. ### Percentage Estimations Based on a Normal Distribution: - **About 68%** of the data falls within one standard deviation of the mean (i.e., between $1750 and $1850). - **About 95%** of the data lies within two standard deviations of the mean (i.e., between $1700 and $1900). - **Approximately 99.7%** falls within three standard deviations of the mean (i.e., between $1650 and $1950). Using the properties of the normal
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