hts per a 12,370. Let X = number o places where possible.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Please answer B, C, and D. 

**Title: Understanding Normal Distribution in Forestry**

**Introduction**
The study of ant populations in forest ecosystems often involves statistical analysis. In this scenario, we examine the distribution of ants per acre in a forest, which follows a normal distribution pattern.

**Distribution Details**
The number of ants per acre in the forest is normally distributed with a mean (μ) of 45,000 and a standard deviation (σ) of 12,370. We represent this distribution as \( X \sim N(45000, 12370^2) \), where \( X \) is the number of ants in a randomly selected acre.

**Problem Analysis**

*a. Distribution Representation*
- \( X \sim N(45000, 12370^2) \)

*b. Probability Calculation (Less than a Given Number)*
- Objective: Find the probability that a randomly selected acre has fewer than 37,630 ants.

*c. Probability Calculation (Within a Range)*
- Objective: Find the probability that the number of ants is between 41,485 and 52,881.

*d. Quartile Calculation*
- Objective: Find the first quartile of the distribution, rounding to the nearest whole number.

**Conclusion**
Understanding these statistical calculations helps in predicting and analyzing the distribution patterns of ants in forest environments, providing insight into ecological balance and health.
Transcribed Image Text:**Title: Understanding Normal Distribution in Forestry** **Introduction** The study of ant populations in forest ecosystems often involves statistical analysis. In this scenario, we examine the distribution of ants per acre in a forest, which follows a normal distribution pattern. **Distribution Details** The number of ants per acre in the forest is normally distributed with a mean (μ) of 45,000 and a standard deviation (σ) of 12,370. We represent this distribution as \( X \sim N(45000, 12370^2) \), where \( X \) is the number of ants in a randomly selected acre. **Problem Analysis** *a. Distribution Representation* - \( X \sim N(45000, 12370^2) \) *b. Probability Calculation (Less than a Given Number)* - Objective: Find the probability that a randomly selected acre has fewer than 37,630 ants. *c. Probability Calculation (Within a Range)* - Objective: Find the probability that the number of ants is between 41,485 and 52,881. *d. Quartile Calculation* - Objective: Find the first quartile of the distribution, rounding to the nearest whole number. **Conclusion** Understanding these statistical calculations helps in predicting and analyzing the distribution patterns of ants in forest environments, providing insight into ecological balance and health.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Matrix Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman