Final answer:
Matt's drums cost the lowest when compared to the average drums, being 1.0 standard deviations below the mean. Becca's guitar costs the highest compared to the average guitar, being 0.25 standard deviations above the mean. Rachel's piano is 0.4 standard deviations below the piano mean.
Step-by-step explanation:
To determine which musical instrument costs the least or the most when compared to other instruments of the same type, we look at how many standard deviations away from the mean each cost is. The formula to find this is (individual cost - mean cost) / standard deviation.
For the piano, with a mean cost of $4,000 and a standard deviation of $2,500, Rachel's piano which cost $3,000 is:
(3,000 - 4,000) / 2,500 = -1 / 2.5 = -0.4 standard deviations below the mean.
For the guitar, with a mean cost of $500 and a standard deviation of $200, Becca's guitar which cost $550 is:
(550 - 500) / 200 = 50 / 200 = 0.25 standard deviations above the mean.
For the drums, with a mean cost of $700 and a standard deviation of $100, Matt's drums which cost $600 is:
(600 - 700) / 100 = -100 / 100 = -1.0 standard deviations below the mean.
Therefore, Matt's drums cost the lowest in comparison to the average drums, and Becca's guitar cost the highest in comparison to the average guitar.