not everyone pays the same price for the same model of a car. the figure illustrates a normal distribution…

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.)

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.)

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, 95% within 2 standard - deviations, and 99.7% within 3 standard - deviations. Mathematically, for a normal distribution with mean $\mu$ and standard deviation $\sigma$, $P(\mu-\sigma<X<\mu + \sigma)\approx0.68$, $P(\mu - 2\sigma<X<\mu+2\sigma)\approx0.95$, $P(\mu - 3\sigma<X<\mu + 3\sigma)\approx0.997$.

Step2: Identify the values of $\mu$ and $\sigma$

Given that $\mu = 22000$ and $\sigma=2000$. The interval from $22000$ to $24000$ is from the mean $\mu$ to $\mu+\sigma$ since $\mu+\sigma=22000 + 2000=24000$.

Step3: Calculate the percentage

The 68% of data within $(\mu-\sigma,\mu+\sigma)$ is symmetric about the mean. So the percentage of data from $\mu$ to $\mu+\sigma$ is half of 68%. That is $\frac{68%}{2}=34%$.

Answer:

34%