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 $19,000 and the standard deviation is $2000. Use the 68-95-99.7 Rule to find what percentage of buyers paid between $15,000 and $19,000.

Answer 1

The percentage of buyers who paid between $15,000 and $19,000 is 47.5%.

Step-by-step explanation:

To find the percentage of buyers who paid between $15,000 and $19,000, we need to find the area under the normal distribution curve between these two prices. First, we calculate the z-scores for both prices using the formula:

z = (x - mean) / standard deviation

For $15,000: z = (15000 - 19000) / 2000 = -2

For $19,000: z = (19000 - 19000) / 2000 = 0

Using a standard normal distribution table, we can find that the percentage of data within 2 standard deviations of the mean is approximately 95%. Since this is a symmetric distribution, we can divide this percentage by 2 to find the percentage between each standard deviation. Therefore, the percentage of buyers who paid between $15,000 and $19,000 is:

95% / 2 = 47.5%