The length of hair of a male private in the army is normally distributed with a mean of 1 cm and a standard deviation of 0.3cm. What is the probability that a male private has hair that is longer than 1.5cm? What is the probability that a male private has hair that is shorter than 1.2cm? What is the probability that male private has hair that is between .5cm and 1.2cm? What is the range of the hair length of the middle 60% of male army privates? inches
The length of hair of a male private in the army is normally distributed with a mean of 1 cm and a standard deviation of 0.3cm. What is the probability that a male private has hair that is longer than 1.5cm? What is the probability that a male private has hair that is shorter than 1.2cm? What is the probability that male private has hair that is between .5cm and 1.2cm? What is the range of the hair length of the middle 60% of male army privates? inches
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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![**Title: Understanding Normal Distribution: Hair Length of Male Army Privates**
**Objective: Calculate Probabilities Using Normal Distribution**
---
**Find Cumulative Probability (CDF)**
- **Min**: \(\infty\)
- **Max**: \(\infty\)
\(\text{inversecdf}( \text{normaldist}(\mu, \sigma)p )\)
The length of hair of a male private in the army is normally distributed with a mean of 1 cm and a standard deviation of 0.3 cm.
---
**Questions:**
1. **What is the probability that a male private has hair that is longer than 1.5 cm?**
\[ \text{Probability} = \_\_\_\_ \]
2. **What is the probability that a male private has hair that is shorter than 1.2 cm?**
\[ \text{Probability} = \_\_\_\_ \]
3. **What is the probability that a male private has hair that is between 0.5 cm and 1.2 cm?**
\[ \text{Probability} = \_\_\_\_ \]
4. **What is the range of the hair length of the middle 60% of male army privates?**
\[ \text{Range} = \_\_\_\_ \text{ inches} \]
---
**Explanation of Normal Distribution:**
Normal distribution is a continuous probability distribution that is symmetrical about its mean, meaning the data near the mean are more frequent in occurrence than data far from the mean. In this case, the hair length of male privates follows a normal distribution with:
- **Mean (\(\mu\))**: 1 cm
- **Standard Deviation (\(\sigma\))**: 0.3 cm
Using these parameters, you can calculate various probabilities and ranges for the hair lengths.
**Graphical Representation:**
If there were a graph or diagram, it would typically show a bell curve centered at 1 cm (mean). The spread of the curve illustrates the standard deviation of 0.3 cm, with most values falling within ±1 standard deviation (0.7 cm to 1.3 cm from the mean).
---
**End of Section**
This section helps you apply the principles of normal distribution to real-world data, enhancing your understanding of probability and statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb845ac35-162e-4da5-a6d5-ce13a46079d9%2F744253e1-82d7-4b21-9a98-3583c6992081%2F21k7wjb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Normal Distribution: Hair Length of Male Army Privates**
**Objective: Calculate Probabilities Using Normal Distribution**
---
**Find Cumulative Probability (CDF)**
- **Min**: \(\infty\)
- **Max**: \(\infty\)
\(\text{inversecdf}( \text{normaldist}(\mu, \sigma)p )\)
The length of hair of a male private in the army is normally distributed with a mean of 1 cm and a standard deviation of 0.3 cm.
---
**Questions:**
1. **What is the probability that a male private has hair that is longer than 1.5 cm?**
\[ \text{Probability} = \_\_\_\_ \]
2. **What is the probability that a male private has hair that is shorter than 1.2 cm?**
\[ \text{Probability} = \_\_\_\_ \]
3. **What is the probability that a male private has hair that is between 0.5 cm and 1.2 cm?**
\[ \text{Probability} = \_\_\_\_ \]
4. **What is the range of the hair length of the middle 60% of male army privates?**
\[ \text{Range} = \_\_\_\_ \text{ inches} \]
---
**Explanation of Normal Distribution:**
Normal distribution is a continuous probability distribution that is symmetrical about its mean, meaning the data near the mean are more frequent in occurrence than data far from the mean. In this case, the hair length of male privates follows a normal distribution with:
- **Mean (\(\mu\))**: 1 cm
- **Standard Deviation (\(\sigma\))**: 0.3 cm
Using these parameters, you can calculate various probabilities and ranges for the hair lengths.
**Graphical Representation:**
If there were a graph or diagram, it would typically show a bell curve centered at 1 cm (mean). The spread of the curve illustrates the standard deviation of 0.3 cm, with most values falling within ±1 standard deviation (0.7 cm to 1.3 cm from the mean).
---
**End of Section**
This section helps you apply the principles of normal distribution to real-world data, enhancing your understanding of probability and statistical analysis.
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