MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.](https://content.bartleby.com/qna-images/question/8eecac97-3428-4be3-91fc-6e8d56624e6a/62c3408c-1f04-4167-a1b3-fbd97388c9a5/qz71s3.jpeg)
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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