$$ { }^{ ext {4 }} $$ A Category: Homework Current score: 91.11/100 points Submi A music school has budgeted to purchase 3 musical instruments. They plan to purchase a plano costing $$ \$ 3000 $$, a guitar costing $$ \$ 550 $$, and a drum set costing $$ \$ 700 $$ The mean cost for a plano is $$ \$ 4000 $$ with a standard deviation of $$ \$ 2000 $$. The mean cost for a guitar is $$ \$ 500 $$ with a standard deviation of $$ \$ 200 $$. The mean cost for drums is $$ \$ 850 $$ with a standard deviation of $$ \$ 100 $$. (Enter your answers to two decimal places.) How many standard deviations above or below the average plano cost is the piano? Enter your answer standard deviations A above the average B below the average How many standard deviations above or below the average guitar cost is the guitar? Enter your answer $$ \square $$ standard deviations A above the average B below the average How many standard deviations above or below the average drum set cost is the drum set? Enter your answer $$ \square $$ standard deviations A below the average

Question

$$ { }^{	ext {4 }} $$ A Category: Homework Current score: 91.11/100 points Submi A music school has budgeted to purchase 3 musical instruments. They plan to purchase a plano costing $$ \$ 3000 $$, a guitar costing $$ \$ 550 $$, and a drum set costing $$ \$ 700 $$ The mean cost for a plano is $$ \$ 4000 $$ with a standard deviation of $$ \$ 2000 $$. The mean cost for a guitar is $$ \$ 500 $$ with a standard deviation of $$ \$ 200 $$. The mean cost for drums is $$ \$ 850 $$ with a standard deviation of $$ \$ 100 $$. (Enter your answers to two decimal places.) How many standard deviations above or below the average plano cost is the piano? Enter your answer standard deviations A above the average B below the average How many standard deviations above or below the average guitar cost is the guitar? Enter your answer $$ \square $$ standard deviations A above the average B below the average How many standard deviations above or below the average drum set cost is the drum set? Enter your answer $$ \square $$ standard deviations A below the average

UpStudy AI · Accepted Answer

Let's calculate the number of standard deviations each instrument's cost is from its respective average.

### 1. Piano
- **Cost of Piano:** \$3,000
- **Mean Cost:** \$4,000
- **Standard Deviation:** \$2,000

**Z-score Calculation:**
$$
Z = \frac{\text{Cost} - \text{Mean}}{\text{Standard Deviation}} = \frac{3000 - 4000}{2000} = \frac{-1000}{2000} = -0.50
$$

**Interpretation:**
- **0.50 standard deviations below the average**

**Answer:**  
**0.50 standard deviations below the average**

---

### 2. Guitar
- **Cost of Guitar:** \$550
- **Mean Cost:** \$500
- **Standard Deviation:** \$200

**Z-score Calculation:**
$$
Z = \frac{550 - 500}{200} = \frac{50}{200} = 0.25
$$

**Interpretation:**
- **0.25 standard deviations above the average**

**Answer:**  
**0.25 standard deviations above the average**

---

### 3. Drum Set
- **Cost of Drum Set:** \$700
- **Mean Cost:** \$850
- **Standard Deviation:** \$100

**Z-score Calculation:**
$$
Z = \frac{700 - 850}{100} = \frac{-150}{100} = -1.50
$$

**Interpretation:**
- **1.50 standard deviations below the average**

**Answer:**  
**1.50 standard deviations below the average**
**Piano:** 0.50 standard deviations below the average **Guitar:** 0.25 standard deviations above the average **Drum Set:** 1.50 standard deviations below the average

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