Question

A music school has budgeted to purchase 3 musical instruments. They plan to purchase a piano costing $4,000, a guitar costing $650, and a drum set costing $800. The mean cost for a piano is $5,000 with a standard deviation of $2,000. The mean cost for a guitar is $550 with a standard deviation of $250. The mean cost for drums is $1100 with a standard deviation of $100. (Enter your answers to two decimal places.)

How many standard deviations above or below the average piano cost is the piano?

____ standard deviations  ---Select--- above below the average

How many standard deviations above or below the average drum set cost is the drum set?

_____ standard deviations  ---Select--- above below the average

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.

Answer 1

Let X be the cost for any given piano. We know that the mean cost for a piano is with a standard deviation of

They plan to purchase a piano costing $4,000. The z score of 4000 is

The negative value indicates that 4000 is 0.5 standard deviations below the mean

How many standard deviations above or below the average piano cost is the piano?

ans: 0.5 standard deviations below the average

The mean cost for drums is $1100 with a standard deviation of $100.

Let Y be the cost for any given drumset. We know that the mean cost for a drumset is with a standard deviation of

They plan to purchase a drumset costing $800. The z score of 800 is

The negative value indicates that 800 is 3 standard deviations below the mean

How many standard deviations above or below the average drum set cost is the drum set?

ans: 3 standard deviations  below the average

Finally, we need the z score for the guitar being bought

The mean cost for a guitar is $550 with a standard deviation of $250 and the guitar costs $650

The z score of 650 is

The positive value indicates that $650 is 0.4 standard deviations above the mean

Which cost is the lowest, when compared to other instruments of the same type?

We can see that drum set being cosnidered has price which is 3 standard deviations lower than the average price of drums. Hene its cost is the lowest

ans: drumset

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

Guitar is 0.4 standard deviations above the mean, where are drums and piano are below the mean. Hence guitar is the most expensive when compared to other instruments of same type.

ans: guitar