Question

note: everyone pays the same price for the same model of a car. the figure shows a particular model of a new car. the mean is $23,000 and the standard deviation is $ percentage of buyers who paid between $23,000 and $26,000. answer: %

Explanation:

Step1: Recall the empirical rule

The empirical rule for a normal distribution states that about 68% of the data is within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Step2: Calculate the number of standard deviations

The mean is \( \mu = 23000 \), and we want to find the value for \( x = 26000 \). Let the standard deviation be \( \sigma \). If \( \mu+3\sigma=26000 \) (since \( 23000 + 3\sigma=26000\), then \( \sigma = 1000 \)).
The interval from the mean (\( 23000 \)) to \( 26000 \) is \( 3\sigma \).
The total area within \( 3\sigma \) of the mean is 99.7%. Due to the symmetry of the normal distribution, the area from the mean to \( 3\sigma \) is \( \frac{99.7\%}{2}=49.85\% \)

Answer:

49.85