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

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!