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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 help with D. Thanks!

Transcribed Image Text:**Title: Understanding Courtship Time Probability in Scorpion Flies**
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**Introduction:**
This educational section focuses on exploring the statistical distribution and probability concerning the courtship time for a randomly selected female-male pair of mating scorpion flies. The data is derived from the article "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognata."
**Details:**
- Let \( X \) denote the courtship time in minutes.
- Mean (\(\mu\)) of \( X \): 120 minutes
- Standard deviation (\(\sigma\)) of \( X \): 110 minutes
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**Analysis:**
**(a) Is it plausible that \( X \) is normally distributed?**
- **Option 1:** Yes, because \( X \) must be negative, and the interval \(\mu \pm 3\sigma\) should be entirely negative. (Incorrect)
- **Option 2:** Yes, because \( X \) has a mean larger than 100. (Incorrect)
- **Option 3:** No, because \( X \) must be non-negative, and \(\mu \pm 3\sigma\) should not overlap with negative values. (Correct)
- **Option 4:** Yes, because \( X \) must be non-negative, and the interval is entirely non-negative. (Correct)
**Conclusion:** \( X \) cannot plausibly be normally distributed because the interval includes negative values, which is non-realistic for courtship time.
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**(b) Probability of Sample Mean Courtship Time (100 min to 125 min)**
- For a random sample of 50 pairs: Probability is approximately **0.5270**. (Correct)
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**(c) Probability of Sample Mean Courtship Time Exceeding 150 min**
- For a random sample of 50 pairs: Needs calculation with proper formula and data adjustment.
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**(d) Central Limit Theorem Application**
- **Question:** Can the result in (b) be calculated for a sample size of 15 instead of 50?
- **Answer:** No, according to guidelines, \( n \) should be greater than 30 to apply the central limit theorem. (Correct)
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This analysis provides insights into statistical applications in biology,
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