The weights of a certain dog breed are approximately normally distributed with a mean of u = 53 pounds, and a standard deviation of o = 5 pounds. %3D
The weights of a certain dog breed are approximately normally distributed with a mean of u = 53 pounds, and a standard deviation of o = 5 pounds. %3D
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Understanding Normal Distribution and the 68-95-99.7 Rule**
The weights of a certain dog breed are approximately normally distributed with a mean (\(\mu\)) of 53 pounds and a standard deviation (\(\sigma\)) of 5 pounds.
**Graph Explanation:**
The graph illustrates a normal distribution curve, which is characterized by its symmetric, bell-shaped appearance. The x-axis includes points labeled as \(\mu - 3\sigma\), \(\mu - 2\sigma\), \(\mu - \sigma\), \(\mu\), \(\mu + \sigma\), \(\mu + 2\sigma\), and \(\mu + 3\sigma\). These represent the mean and standard deviations from the mean.
Each section of the graph denotes ranges, where the weights fall within certain standard deviations from the mean:
- **\(\mu - 3\sigma\) to \(\mu + 3\sigma\)** covers 99.7% of the data.
- **\(\mu - 2\sigma\) to \(\mu + 2\sigma\)** covers 95% of the data.
- **\(\mu - \sigma\) to \(\mu + \sigma\)** covers 68% of the data.
**Numerical Calculations:**
1. \(\mu = 53\), \(\sigma = 5\)
Fill in the boxes based on standard deviations:
- \(\mu - 3\sigma = 53 - 15 = 38\)
- \(\mu - 2\sigma = 53 - 10 = 43\)
- \(\mu - \sigma = 53 - 5 = 48\)
- \(\mu + \sigma = 53 + 5 = 58\)
- \(\mu + 2\sigma = 53 + 10 = 63\)
- \(\mu + 3\sigma = 53 + 15 = 68\)
**Z-Score Calculation:**
A dog of this breed weighs 56 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed.
The z-score can be calculated using the formula:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \(X\) is the observed value (56 pounds).
- \(\mu\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc24d0110-74e6-4765-afd2-6bfe95475961%2Fc2e1a54c-3752-440b-af15-6c7be02d60d2%2F430qtt2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Normal Distribution and the 68-95-99.7 Rule**
The weights of a certain dog breed are approximately normally distributed with a mean (\(\mu\)) of 53 pounds and a standard deviation (\(\sigma\)) of 5 pounds.
**Graph Explanation:**
The graph illustrates a normal distribution curve, which is characterized by its symmetric, bell-shaped appearance. The x-axis includes points labeled as \(\mu - 3\sigma\), \(\mu - 2\sigma\), \(\mu - \sigma\), \(\mu\), \(\mu + \sigma\), \(\mu + 2\sigma\), and \(\mu + 3\sigma\). These represent the mean and standard deviations from the mean.
Each section of the graph denotes ranges, where the weights fall within certain standard deviations from the mean:
- **\(\mu - 3\sigma\) to \(\mu + 3\sigma\)** covers 99.7% of the data.
- **\(\mu - 2\sigma\) to \(\mu + 2\sigma\)** covers 95% of the data.
- **\(\mu - \sigma\) to \(\mu + \sigma\)** covers 68% of the data.
**Numerical Calculations:**
1. \(\mu = 53\), \(\sigma = 5\)
Fill in the boxes based on standard deviations:
- \(\mu - 3\sigma = 53 - 15 = 38\)
- \(\mu - 2\sigma = 53 - 10 = 43\)
- \(\mu - \sigma = 53 - 5 = 48\)
- \(\mu + \sigma = 53 + 5 = 58\)
- \(\mu + 2\sigma = 53 + 10 = 63\)
- \(\mu + 3\sigma = 53 + 15 = 68\)
**Z-Score Calculation:**
A dog of this breed weighs 56 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed.
The z-score can be calculated using the formula:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \(X\) is the observed value (56 pounds).
- \(\mu\
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