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 new car. the mean is $21,000 and the standard deviation is $1000. use the 68 - 95 - 99.7 rule to find what percentage of buyers paid between $21,000 and $22,000. the percentage of buyers who paid between $21,000 and $22,000 is % (type an exact answer.)

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# Explanation:
## Step1: Recall the 68 - 95 - 99.7 Rule
The 68 - 95 - 99.7 Rule states that for a normal distribution:
- Approximately 68% of the data lies within $1$ standard deviation ($\mu\pm\sigma$) of the mean.
- Approximately 95% of the data lies within $2$ standard deviations ($\mu\pm2\sigma$) of the mean.
- Approximately 99.7% of the data lies within $3$ standard deviations ($\mu\pm3\sigma$) of the mean.

## Step2: Analyze the range
Given $\mu = 21000$ and $\sigma=1000$. The range $21000$ to $22000$ is $\mu$ to $\mu + \sigma$.
Since the normal distribution is symmetric about the mean, the percentage of data within $\mu-\sigma$ and $\mu+\sigma$ is 68%. The percentage of data from $\mu$ to $\mu+\sigma$ is half of the percentage of data from $\mu - \sigma$ to $\mu+\sigma$.

## Step3: Calculate the required percentage
We know that $P(\mu-\sigma<X<\mu+\sigma)=68\%$. Then $P(\mu<X<\mu + \sigma)=\frac{68\%}{2}$

$$P(21000<X<22000)=\frac{68}{2}=34\%$$

# Answer:
34

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Question

Explanation:

Step1: Recall the 68 - 95 - 99.7 Rule

Step2: Analyze the range

Step3: Calculate the required percentage

Answer: