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

A z-score can be placed on a normal distribution curve. By using the z-score statistical tool we can analyze the lowest cost and highest cost a given in case the mean and standard deviation of a normal distribution is given.

What is a Z-score?

Z-score (also called standard points) gives you an idea of how far from the mean the data point is. But technically it is a measure of how many standard deviations are below or above the population means the raw score.

A z-score of 1 is 1 standard deviation above the mean.
A z- score of 2 is 2 standard deviations above the mean.
A z-score of -1.8 is -1.8 standard deviations below the mean.

As per the given information, we need to calculate the z-score value, which is as follows:

[tex]\rm\,Z= \frac{X(Value \,Given) - Mean}{Sigma\,(Standard\,Deviation)}[/tex]

After putting the values,

[tex]\rm\, Z= \frac{X(Value \,Given) - Mean}{Sigma\,(Standard\,Deviation)} \\\\For\,piano, Z = \frac{X - Mean}{Sigma} \\\\Z = \frac{3,000 - 4,000 }{2,500} \\\\Z = - 0.4\\\\For\,Guitar, Z =\frac{X - Mean}{Sigma} \\\\Z =\frac{550- 500}{200} \\\\Z = 0.25\\\\For\,Drums\,Set, Z = \rm\,\dfrac{\rm\,X - Mean}{\rm\,Sigma}\\Z = \rm\,\dfrac{\rm\,600 - 700}{\rm\,100}\\\\Z = -1[/tex]

Therefore, Drum set cost is the lowest among others, -1 standard deviations below the mean whereas Guitar has the highest cost, 1 standard deviation above the mean.

To learn more about Z-score, refer to the link:

https://brainly.com/question/25638875