(a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places.) at most 100 m at most 200 m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.) (c) What is the value of the median distance? (Round your answer to two decimal places.)
(a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places.) at most 100 m at most 200 m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.) (c) What is the value of the median distance? (Round your answer to two decimal places.)
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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![**Exponential Distribution and Animal Movement**
**Context**: Consider the random variable \( X \) which denotes the distance (in meters) that an animal, specifically a banner-tailed kangaroo rat, moves from its birth site to the first territorial vacancy it encounters. The distance \( X \) follows an exponential distribution with a parameter \( \lambda = 0.01417 \).
**Tasks and Questions**:
**(a)** Calculate the probabilities for the following scenarios (provide answers rounded to four decimal places):
1. What is the probability that the distance is at most 100 meters?
- **At most 100 m**: [ ]
2. What is the probability that the distance is at most 200 meters?
- **At most 200 m**: [ ]
3. What is the probability that the distance is between 100 and 200 meters?
- **Between 100 and 200 m**: [ ]
**(b)** Determine the probability that the distance exceeds the mean distance by more than 2 standard deviations. Provide your answer rounded to four decimal places.
- **Exceeds mean by more than 2 SD**: [ ]
**(c)** Calculate the value of the median distance. Provide your answer rounded to two decimal places.
- **Median distance**: [ ] m
In this exercise, you are exploring the properties of the exponential distribution, a common model for processes that have a constant hazard rate. Understanding these probabilities and values helps in modeling and analyzing real-world phenomena such as animal movement patterns.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7e43dbe-ab72-46fa-955b-a8f42ce6613a%2Fefd383c4-c082-4333-8b40-00d03d5b5a4b%2Fnemnt1i_processed.png&w=3840&q=75)
Transcribed Image Text:**Exponential Distribution and Animal Movement**
**Context**: Consider the random variable \( X \) which denotes the distance (in meters) that an animal, specifically a banner-tailed kangaroo rat, moves from its birth site to the first territorial vacancy it encounters. The distance \( X \) follows an exponential distribution with a parameter \( \lambda = 0.01417 \).
**Tasks and Questions**:
**(a)** Calculate the probabilities for the following scenarios (provide answers rounded to four decimal places):
1. What is the probability that the distance is at most 100 meters?
- **At most 100 m**: [ ]
2. What is the probability that the distance is at most 200 meters?
- **At most 200 m**: [ ]
3. What is the probability that the distance is between 100 and 200 meters?
- **Between 100 and 200 m**: [ ]
**(b)** Determine the probability that the distance exceeds the mean distance by more than 2 standard deviations. Provide your answer rounded to four decimal places.
- **Exceeds mean by more than 2 SD**: [ ]
**(c)** Calculate the value of the median distance. Provide your answer rounded to two decimal places.
- **Median distance**: [ ] m
In this exercise, you are exploring the properties of the exponential distribution, a common model for processes that have a constant hazard rate. Understanding these probabilities and values helps in modeling and analyzing real-world phenomena such as animal movement patterns.
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