Final answer:
Marvin should evaluate additional factors such as the car's condition, history, and potential extra costs or benefits, not just price. If all other factors are equal, the cheaper car may be preferred, but the more expensive option could offer better value if it includes warranties or recent maintenance. Used car sales costs can be analyzed using the normal distribution when the sample size is sufficiently large.
Step-by-step explanation:
When Marvin is deciding which used car to buy, he should consider factors beyond just price, mileage, exterior appearances, and age. These could include the car's overall condition, reliability, maintenance history, cost of ownership (including insurance, taxes, and expected repair costs), and potentially resale value.
If both vehicles appear to be in similar condition and have comparable features, Marvin might lean towards the less expensive option, saving $600.
However, if the more expensive car has a better service history or comes with additional perks like a dealer warranty or recent maintenance, the extra cost could be justified. Making a decision purely based on price might not always be the best long-term choice.
Analyzing the costs of used car sales can be done using a normal distribution, particularly if the sample size is large and the underlying distribution of prices is not known to be significantly non-normal.
So for the second scenario provided, since the sample size of 84 used car sales is moderately large, we can approximate the underlying distribution as normal due to the Central Limit Theorem.
This is because the sample mean can be considered normally distributed regardless of the shape of the underlying population distribution when the sample size is sufficiently large.