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

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

MATLAB: An Introduction with Applications
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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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.
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