Please help with D. Thanks! **Title: Understanding Courtship Time Probability in Scorpion Flies**---**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---**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.---**(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)---**(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.---**(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)---**Need Further Assistance?**For more in-depth understanding and explanations, click "Read It".---This analysis provides insights into statistical applications in biology,

Name: Please help with D. Thanks! **Title: Understanding Courtship Time Prob
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help with D. Thanks! **Title: Understanding Courtship Time Probability in Scorpion Flies**---**Introduction:**This educational section focuses on exploring the statistical distribution and probability concerning the courtship time for a random

Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies. Given, μx=120σx=110 a). No, courtship time cannot plausibly be normally distributed, since x must be non-negative ,realistically the interval μ±3σ should be entirely non-negative which is not true in this case. b). Here n=50, Therefore, the required probability that the sample mean courtship time is between 100 min and 120 min is obtained as- P100<x<125=P100-12011050<x-μxσxn<125-12011050=P-1.2856<z<0.32141=Pz<0.32141-Pz<-1.2856=0.62605-0.099291 From z-distribution table=0.526759c). The required probability that the sample mean courtship time exceeds 150 min is obtained as- Px>150=Px-μσn>150-12011050=Pz>1.9285=1-Pz<1.9285=1-0.9731=0.0269 d). No, according to the guideline n should be greater than 30 in order to apply the central limit theorem.