A music school has budgeted to purchase 3 musical instruments. they plan to purchase a piano costing $4,000, a guitar costing $600, and a drum set costing $750. 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 $950 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

Question

Karissa Powers

Mathematics

6 February, 00:32

A music school has budgeted to purchase 3 musical instruments. they plan to purchase a piano costing $4,000, a guitar costing $600, and a drum set costing $750. 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 $950 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

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Nigel · Answer 1

To solve this, we can use the z statistic. The formula for z score is given as:

z = (x - u) / s

where x is the actual cost = 4000, u is the mean cost = 5000, and s is the standard deviation = 2000

Solving for z:

z = (4000 - 5000) / 2000

z = - 0.5

Therefore the piano cost is only 0.5 standard deviations below the average cost.