Final answer:
Using standard deviations, the drums priced at $600 are the lowest cost being 1.0 standard deviations below the mean. The guitar at $550 is the highest cost at 0.25 standard deviations above the mean. The piano is priced lower than average at 0.4 standard deviations below the mean.
Step-by-step explanation:
When comparing the cost of musical instruments to the average cost of that instrument type, we use the standard deviation from the mean to determine how the cost of the instrument purchased by the music school or individual compares to the typical cost of that instrument. The mean and standard deviation give us a way to understand the distribution of instrument costs and the position of a specific cost within that distribution.
In this case for the piano costing $3,000: since the mean cost is $4,000 with a standard deviation of $2,500, this places the piano cost 0.4 standard deviations BELOW the mean. This indicates that the piano is priced lower than the average piano. For the guitar costing $550: the mean cost is $500 with a standard deviation of $200, which means the guitar is 0.25 standard deviations ABOVE the mean, indicating it is slightly more expensive than the average guitar. Lastly, the drum set costing $600 has a mean cost of $700 with a standard deviation of $100, which places it at 1.0 standard deviations BELOW the mean, suggesting it is significantly cheaper than the average price for drums.
Therefore, the drum set is considered the lowest cost relative to the other drum sets on the market, while the guitar has the highest cost in comparison to other guitars.