Final answer:
Reducing each car's price by a flat $500 will lower the center and maintain the shape and variability of the price distribution. Discounting cars by an additional 10% will further reduce the center, potentially alter the shape slightly, and increase the variability due to higher-priced cars receiving larger discounts in dollar terms.
Step-by-step explanation:
If a used car salesman reduces the price of each car by $500, this will shift the entire distribution of car prices downwards by $500. This means the shape of the distribution will remain the same, as each value is decreased uniformly. The center of the distribution, often measured as the mean or median, will also decrease by $500. However, the variability of the distribution, often quantified by the range or standard deviation, will not change because the reduction is consistent across all prices. For the additional discount of 10%, because it is a proportional discount, the effect on the distribution depends on the initial prices of the cars. In general, higher-priced cars will receive a larger dollar amount discount compared to lower-priced cars. This means that the distribution will become slightly more spread out, as the variability increases. The center will again shift downwards, this time by 10% of the average price. The shape of the distribution may slightly change, especially if the initial distribution was not uniform because the proportional discount affects higher values more than lower ones.