A music school has budgeted to purchase three musical instruments. They plan to purchase a piano costing \($3,000\), a guitar costing \($550\), and a drum set costing \($600\). The mean cost for a piano is \($4,000\) with a standard deviation of $2,500.

The mean cost for a guitar is \($500\) with a standard deviation of \($200\). The mean cost for drums is \($700\) with a standard deviation of \($100\). Which cost is the lowest, when compared to other instruments of the same type? Which cost is the highest when compared to other instruments of the same type. Justify your answer.