The sales of Adidas have been fluctuating over the few years. When put on analysis, it showed a bell shaped distribution with a mean of 100 and a standard deviation of 15. You have been hired by Adidas to find: What is the range of z scores for sales between 85 and 130? Choose: A) [-2,2] B) [85,115] C) [-1,2] D) [85,130] E) [-1,1]

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**Sales Data Analysis for Adidas**

The sales of Adidas have been fluctuating over the past few years. Upon analysis, it was determined that the sales data follows a bell-shaped distribution with a mean of 100 and a standard deviation of 15. As an analyst, you have been hired by Adidas to find out specific information regarding the sales distribution. 

**Problem Statement**

What is the range of z-scores for sales between 85 and 130?

**Select One of the Following Options:**

A) [-2, 2]

B) [85, 115]

C) [-1, 2]

D) [85, 130]

E) [-1, 1]

---

**Explanation:**
- The problem involves finding the z-scores for given sales values when the sales follow a normal distribution.
- The z-score is a measure of how many standard deviations a data point is from the mean.
  
**Links and Helpful Concepts:**
- **Bell-shaped Distribution**: [Read more](https://www.example.com/link_to_more_explained_data)
- **Finding Z-scores**: To find the z-score, use the formula: 
  \[ z = \frac{(X - \mu)}{\sigma} \]
  where \(X\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

**Steps to Compute Z-scores:**
1. For \(X = 85\):
   \[ z = \frac{(85 - 100)}{15} = \frac{-15}{15} = -1 \]
2. For \(X = 130\):
   \[ z = \frac{(130 - 100)}{15} = \frac{30}{15} = 2 \]

Hence, the range of z-scores is \([-1, 2]\).

---

**Correct Answer:**

C) \([-1, 2]\)

This analysis allows understanding how sales data points deviate from the mean and underlines the importance of normal distribution in sales data assessment.
Transcribed Image Text:**Sales Data Analysis for Adidas** The sales of Adidas have been fluctuating over the past few years. Upon analysis, it was determined that the sales data follows a bell-shaped distribution with a mean of 100 and a standard deviation of 15. As an analyst, you have been hired by Adidas to find out specific information regarding the sales distribution. **Problem Statement** What is the range of z-scores for sales between 85 and 130? **Select One of the Following Options:** A) [-2, 2] B) [85, 115] C) [-1, 2] D) [85, 130] E) [-1, 1] --- **Explanation:** - The problem involves finding the z-scores for given sales values when the sales follow a normal distribution. - The z-score is a measure of how many standard deviations a data point is from the mean. **Links and Helpful Concepts:** - **Bell-shaped Distribution**: [Read more](https://www.example.com/link_to_more_explained_data) - **Finding Z-scores**: To find the z-score, use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \(X\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. **Steps to Compute Z-scores:** 1. For \(X = 85\): \[ z = \frac{(85 - 100)}{15} = \frac{-15}{15} = -1 \] 2. For \(X = 130\): \[ z = \frac{(130 - 100)}{15} = \frac{30}{15} = 2 \] Hence, the range of z-scores is \([-1, 2]\). --- **Correct Answer:** C) \([-1, 2]\) This analysis allows understanding how sales data points deviate from the mean and underlines the importance of normal distribution in sales data assessment.
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