Current score: 93.36/100 points Submi A music school has budgeted to purchase 3 musical instruments. They plan to purchase a piano costing $$ \$ 3000 $$, a guitar costing $$ \$ 550 $$, and a drum set costing $$ \$ 700 $$ The mean cost for a piano 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 piano cost is the piano? 0.75 (1) standard deviations A above the average B below the average © Your answer is correct. How many standard deviations above or below the average guitar cost is the guitar? 0.25 standard deviations A above the average B below the average Your answer is correct. How many standard deviations above or below the average drum set cost is the drum set? $$ -1.50 $$ $$ \square $$ standard deviations

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Let's verify your calculations for each musical instrument by determining how many standard deviations each purchase price is above or below the average cost.

### 1. **Piano**
- **Purchase Price:** \$3,000
- **Mean Cost:** \$4,000
- **Standard Deviation (SD):** \$2,000

**Calculation:**
$$
z = \frac{\text{Purchase Price} - \text{Mean Cost}}{\text{SD}} = \frac{3000 - 4000}{2000} = \frac{-1000}{2000} = -0.50
$$

**Interpretation:**
- **-0.50 SD** below the average.

**Correction Needed:**
You mentioned **0.75 SD below the average**, but the correct value is **-0.50 SD below the average**.

---

### 2. **Guitar**
- **Purchase Price:** \$550
- **Mean Cost:** \$500
- **Standard Deviation (SD):** \$200

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

**Interpretation:**
- **0.25 SD** above the average.

**Your Answer:**
- **0.25 SD above the average** *(Correct)*

---

### 3. **Drum Set**
- **Purchase Price:** \$700
- **Mean Cost:** \$850
- **Standard Deviation (SD):** \$100

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

**Interpretation:**
- **-1.50 SD** below the average.

**Your Answer:**
- **-1.50 SD below the average** *(Correct)*

---

### **Summary of Correct Answers:**
1. **Piano:** **-0.50 standard deviations below** the average.
2. **Guitar:** **0.25 standard deviations above** the average.
3. **Drum Set:** **-1.50 standard deviations below** the average.

Ensure to use the correct z-scores based on the calculations above. If you have any further questions or need additional assistance, feel free to ask!
**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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