Question

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 $22,000 and the standard deviation is $2000. use the 68 - 95 - 99.7 rule to find what percentage of buyers paid between $22,000 and $24,000. the percentage of buyers who paid between $22,000 and $24,000 is %. (type an exact answer.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule states that in a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), about 95% lies within 2 standard - deviations of the mean ($\mu\pm2\sigma$), and about 99.7% lies within 3 standard - deviations of the mean ($\mu\pm3\sigma$). The normal distribution is symmetric about the mean.

Step2: Identify the mean and standard deviation

Given that the mean $\mu = 22000$ and the standard deviation $\sigma=2000$. The value $24000$ can be written as $\mu+\sigma$ since $22000 + 2000=24000$.

Step3: Determine the percentage

Since the normal distribution is symmetric about the mean, the percentage of data between $\mu$ and $\mu + \sigma$ is half of the percentage of data between $\mu-\sigma$ and $\mu+\sigma$. The percentage of data between $\mu-\sigma$ and $\mu+\sigma$ is 68%. So the percentage of data between $\mu$ and $\mu+\sigma$ is $\frac{68\%}{2}=34\%$.

Answer:

34%