Question

ily wants to sell her violin, which she has kept in excellent condition. Ordinarily, this type of violin sells second hand for $4000, but as Lily has looked after hers extremely well, she determine whether Lily's violin is in good condition or not. Answer the following questions: a. Thinking like an economist, would Natalie definitely buy the violin from Lily?

Answer 1

To find the cost that is the lowest when compared to other instruments of the same type, calculate the z-scores for Rachel's piano, Becca's guitar, and Matt's drums. Matt's drums have the lowest z-score, indicating his cost is the lowest relative to the typical cost of drums. Without further differentiating factors, Marvin would likely choose the less expensive car.

Step-by-step explanation:

The question is about comparing the costs of Rachel's piano, Becca's guitar, and Matt's drums against the average costs and standard deviations of those musical instruments. To determine whose cost was lowest relative to the standard distribution for each instrument type, we calculate how many standard deviations each purchase is from the mean cost. This measure is called a z-score, which indicates how far and in what direction, an individual observation lies from its distribution's mean, measured in standard deviations.

Rachel’s piano cost $3,000 while the average is $4,000 with a standard deviation of $2,500. This gives a z-score of (3,000 - 4,000) / 2,500 = -0.4.

Becca’s guitar cost $550 with the average at $500 and a standard deviation of $200. This gives us a z-score of (550 - 500) / 200 = 0.25.

Matt’s drums cost $600, with the average price at $700 and a standard deviation of $100. The z-score is (600 - 700) / 100 = -1.

Comparing these z-scores helps us identify the cost that is the lowest relative to its own instrument type: Matt's drums have the lowest z-score at -1, indicating his cost is the lowest when compared to the typical cost of drums.

When Marvin shops for a used car, the decision to buy the one costing $4,000 or $4,600 should be based on more than just price. Marvin should consider factors such as the car's condition, history, and any potential additional costs that might not be immediately apparent. Without more information to differentiate the cars other than mileage, exterior appearances, and age, which are similar, a rational choice would be to choose the less expensive option, given that all other factors are equal.