A music school has budgeted to purchase three musical instruments. They plan to purchase a piano costing $3,000, aguitar 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 astandard deviation of 5100. Which cost is the lowest, when compared to other instruments of the same type? Which cost isthe highest when compared to other instruments of the same type. Justify your answer.

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zainsubhani zainsubhani · Answer 1 · 2020-02-07T18:35:43+01:00

Answer:

Lowest Cost is for Drum set, when compared to others instruments of same type.

Highest cost is for Guitar,when compared to others instruments of same type.

Order:

Guitar>Piano>Drum Set

Step-by-step explanation:

Consider the normal distribution for all cases.

Formula we are going to use is:

[tex]z=\frac{\bar x-\mu}{\sigma}[/tex]

where:

[tex]\bar x[/tex] is the purchasing cost

[tex]\mu[/tex] is the mean

[tex]\sigma[/tex] is the standard deviation

For Piano:

[tex]z=\frac{3000-4000}{2500}\\ z=-0.4[/tex]

For Guitar:

[tex]z=\frac{550-500}{200}\\ z=0.25[/tex]

For Drum Set:

[tex]z=\frac{600-700}{100}\\ z=-1[/tex]

Lowest Cost is for Drum set, when compared to others instruments of same type.

Highest cost is for Guitar,when compared to others instruments of same type.

Order:

Guitar>Piano>Drum Set