Question

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

Answer 1

Assuming the costs are normally distributed, then Z = (X-mu)/sigma

For piano Z= (3000-4000)/2500 = -0.4

For guitar Z= (550-500)/200 = 0.25

For drums set Z= (600-700)/100 = -1

Drums set < Piano < Guitar

Drums cost is lowest when compared to the instruments of same type .

Guitar cost is highest when compared to the instruments of same type.