Question

Marwick's Pianos, Incorporated, purchases pianos from a large manufacturer for an average cost of $ ____ per unit and then sells them to retail customers for an average price of $ _____.

Answer 1

By calculating the z-scores, we find that Matt's drums have the lowest cost relative to the average for drums, while Becca's guitar has the highest cost compared to the average for guitars.

Step-by-step explanation:

In order to determine whose instrument cost is the lowest when compared to the average cost of their respective instrument, we need to calculate how many standard deviations below or above the mean each cost is, which is known as the z-score. A lower z-score indicates a cost further below the mean, signifying a better deal in comparison to the typical price for that instrument. Rachel's piano cost $3,000, compared to an average piano price of $4,000 with a standard deviation of $2,500. The z-score for Rachel's piano is (3000 - 4000) / 2500 = -0.4. Becca's guitar cost $550, with an average of $500 and a standard deviation of $200, making the z-score (550 - 500) / 200 = 0.25. Lastly, Matt's drums cost $600, while the average cost for drums is $700 with a standard deviation of $100. This gives us a z-score of (600 - 700) / 100 = -1. Therefore, Matt's drums have the lowest cost compared to the average, and Becca's guitar has the highest cost relative to the average.