Questions: Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a now car. The mean is 19,000 and the standard deviation is 2,000. Use the 68-95-99.7 Rule to find what percentage of buyers paid between 17,000 and 21,000. The percentage of buyers who paid between 17,000 and 21,000 is %.

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a now car. The mean is 19,000 and the standard deviation is 2,000. Use the 68-95-99.7 Rule to find what percentage of buyers paid between 17,000 and 21,000. The percentage of buyers who paid between 17,000 and 21,000 is %.
Transcript text: Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a now car. The mean is $\$ 19,000$ and the standard deviation is $\$ 2000$. Use the 68-95-99.7 Rule to find what percentage of buyers paid between $\$ 17,000$ and $\$ 21,000$. The percentage of buyers who paid between $\$ 17,000$ and $\$ 21,000$ is $\square$ $\%$.
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Solution

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Solution Steps

Step 1: Identify the mean and standard deviation.

The problem states that the mean price is $19,000 and the standard deviation is $2,000.

Step 2: Determine the range of prices within one standard deviation of the mean.

One standard deviation below the mean is: $19,000 - $2,000 = $17,000

One standard deviation above the mean is: $19,000 + $2,000 = $21,000

Step 3: Apply the 68-95-99.7 Rule.

The 68-95-99.7 Rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean. Since the range of $17,000 to $21,000 represents one standard deviation below and above the mean, respectively, we can conclude that 68% of buyers paid within this price range.

Final Answer

\\(\boxed{68}\\)

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