\( { }^{\text {4 }} \) 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

To find how many standard deviations each instrument's cost is from the mean, we use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the cost of the instrument, \( \mu \) is the mean cost, and \( \sigma \) is the standard deviation. 1. For the piano: - \( X = 3000 \), \( \mu = 4000 \), \( \sigma = 2000 \) \[ z = \frac{(3000 - 4000)}{2000} = \frac{-1000}{2000} = -0.5 \] Thus, the piano is **0.50 standard deviations below the average**. 2. For the guitar: - \( X = 550 \), \( \mu = 500 \), \( \sigma = 200 \) \[ z = \frac{(550 - 500)}{200} = \frac{50}{200} = 0.25 \] Thus, the guitar is **0.25 standard deviations above the average**. 3. For the drum set: - \( X = 700 \), \( \mu = 850 \), \( \sigma = 100 \) \[ z = \frac{(700 - 850)}{100} = \frac{-150}{100} = -1.5 \] Hence, the drum set is **1.50 standard deviations below the average**. Now, let's write down the final answers: For the piano: **0.50 standard deviations below the average** For the guitar: **0.25 standard deviations above the average** For the drum set: **1.50 standard deviations below the average** If you need to round to two decimal places, you can simply keep it as stated. Happy studying!