### Assessing the Sample Mean of Magic Rabbits' Weight**Concept: Normal Distribution**- According to the Official Stage Magician Handbook, magic rabbit weight (in pounds) follows a normal distribution.- The distribution is characterized by: - Mean (μ) = 6.2 lbs. - Standard Deviation (σ) = 1.5 lbs.**Scenario: Random Sampling**- Consider obtaining a random sample of 3 magic rabbits.- The goal is to determine if it would be unusual for the sample mean to be at least 6.5 lbs.**Question: Unusual Sample Mean?**- Would it be unusual for the sample mean to be at least 6.5? Why or why not?**Answer Choices:**1. **Yes**, because the z-score corresponding to a sample mean of 6.5 would be $ z = 0.34 $.2. **No**, because the z-score corresponding to a sample mean of 6.5 would be $ z = 0.34 $.3. **Yes**, because the z-score corresponding to a sample mean of 6.5 would be $ z = 0.20 $.4. **No**, because the z-score corresponding to a sample mean of 6.5 would be $ z = 0.20 $.**Explanation:**- To answer this, we calculate the z-score for the sample mean of 6.5. The formula for the z-score of the sample mean is:\[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \]Where:- $\bar{x}$ = Sample mean- $\mu$ = Population mean- $\sigma$ = Population standard deviation- $n$ = Sample sizeSubstituting the values:- $\bar{x} = 6.5$- $\mu = 6.2$- $\sigma = 1.5$- $n = 3$\[ z = \frac{6.5 - 6.2}{\frac{1.5}{\sqrt{3}}} \]\[ z = \frac{0.3}{0.866} \]\[ z \approx 0.35 \]So, the z-score should be approximately 0.35.To

The Z-score for the sample mean of the random variable equals 6.5 is 0.34.

According to the Official Stage Magician Handbook, magic rabbit weight (Ibs.) is normally distributed with u = 6.2 and o = 1.5. Consider obtaining a random sample of 3 magic rabbits. Would it be unusual for the sample mean to be at least 6.5? Why or why not? Yes because the z-score corresponding to a sample mean of 6.5 would be z = 0.34. No because the z-score corresponding to a sample mean of 6.5 would be z = 0.34. O Yes because the z-score corresponding to a sample mean of 6.5 would be z =0.20. O No because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.

According to the Official Stage Magician Handbook, magic rabbit weight (Ibs.) is normally distributed with u = 6.2 and o = 1.5. Consider obtaining a random sample of 3 magic rabbits. Would it be unusual for the sample mean to be at least 6.5? Why or why not? Yes because the z-score corresponding to a sample mean of 6.5 would be z = 0.34. No because the z-score corresponding to a sample mean of 6.5 would be z = 0.34. O Yes because the z-score corresponding to a sample mean of 6.5 would be z =0.20. O No because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.

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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