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 $23,000 and the standard deviation is $1000. 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 (%). number of car buyers price of a model of a new car (thousands)

Explanation:

Step1: Calculate the z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value. Given $\mu = 23000$, $\sigma=1000$. For $x = 22000$, $z_1=\frac{22000 - 23000}{1000}=- 1$. For $x = 24000$, $z_2=\frac{24000 - 23000}{1000}=1$.

Step2: Apply 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 of the mean. That is, the percentage of data between $z=-1$ and $z = 1$ is 68%.

Answer:

68