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?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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![### 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2daf47f-1d43-4c0e-a218-05866800687b%2Fafb9c42b-3eef-42ae-aa77-b0fe21c8bd44%2Fn8cvcep.jpeg&w=3840&q=75)
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