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We are asked to find the percentage of car buyers who paid less than $22,000 using the 68-95-99.7 rule (also known as the empirical rule). The given information is:

- **Mean price** = $24,000
- **Standard deviation** = $2,000

The empirical rule states:
- 68% of data lies within 1 standard deviation (±1σ) of the mean.
- 95% of data lies within 2 standard deviations (±2σ) of the mean.
- 99.7% of data lies within 3 standard deviations (±3σ) of the mean.

### Step-by-Step Breakdown:
1. **Mean = $24,000** and **standard deviation (σ) = $2,000**.
2. **$22,000** is **$2,000 less than the mean**, which means it is **1 standard deviation below the mean**.
3. According to the 68-95-99.7 rule, 68% of the data lies between $22,000 and $26,000, so half of this (34%) lies between $22,000 and the mean ($24,000).
4. Since the normal distribution is symmetric, 50% of buyers are below the mean, and from this 50%, we subtract the 34% who paid between $22,000 and $24,000.
   
   Thus, the percentage of buyers who paid less than $22,000 is:

   \[
   50\% - 34\% = 16\%
   \]

So, **16%** of buyers paid less than $22,000.

Would you like more details on this or have further questions?

Here are five related questions:
1. What percentage of buyers paid more than $28,000?
2. How do we find the percentage of buyers who paid between $20,000 and $24,000?
3. What is the probability that a buyer paid between $22,000 and $28,000?
4. How would the results change if the standard deviation was larger?
5. How does the 68-95-99.7 rule apply to non-symmetric distributions?

**Tip:** The empirical rule is a quick estimation tool but may not give exact values for non-normally distributed data!

What percentage of car buyers paid less than $22,000 based on a normal distribution with a mean price of $24,000 and a standard deviation of $2,000?

Learn how to calculate the percentage of car buyers who paid less than $22,000 for a car using a normal distribution with a mean of $24,000 and standard deviation of $2,000. This problem applies the 68-95-99.7 rule.

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