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 9 magic rabbits. Would it be unusual for the sample mean to be at least 6.5? Why or why not? No because the z-score corresponding to a sample mean of 6.5 would be z = 0.20. O Yes because the z-score corresponding to a sample mean of 6.5 would be z = 0.60. O No because the z-score corresponding to a sample mean of 6.5 would be z = 0.60. Yes 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 9 magic rabbits. Would it be unusual for the sample mean to be at least 6.5? Why or why not? No because the z-score corresponding to a sample mean of 6.5 would be z = 0.20. O Yes because the z-score corresponding to a sample mean of 6.5 would be z = 0.60. O No because the z-score corresponding to a sample mean of 6.5 would be z = 0.60. Yes because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.
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Question
![**Understanding Z-Scores and Sample Means**
According to the Official Stage Magician Handbook, magic rabbit weight (in pounds) is normally distributed with a mean (μ) of 6.2 and a standard deviation (σ) of 1.5.
Consider obtaining a random sample of 9 magic rabbits.
**Question:**
Would it be unusual for the sample mean to be at least 6.5? Why or why not?
**Choices:**
1. No, because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.
2. Yes, because the z-score corresponding to a sample mean of 6.5 would be z = 0.60.
3. No, because the z-score corresponding to a sample mean of 6.5 would be z = 0.60.
4. Yes, because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.
**Explanation:**
- **Mean (μ):** 6.2
- **Standard Deviation (σ):** 1.5
- **Sample Size (n):** 9
- **Sample Mean (X̄):** 6.5
To determine if it is unusual for the sample mean to be at least 6.5, we need to calculate the z-score. The formula for the z-score for a sample mean is:
\[ z = \frac{X̄ - μ}{\frac{σ}{\sqrt{n}}} \]
Given the values:
\[ z = \frac{6.5 - 6.2}{\frac{1.5}{\sqrt{9}}} \]
First, calculate the standard error (SE):
\[ SE = \frac{σ}{\sqrt{n}} = \frac{1.5}{\sqrt{9}} = \frac{1.5}{3} = 0.5 \]
Now, calculate the z-score:
\[ z = \frac{6.5 - 6.2}{0.5} = \frac{0.3}{0.5} = 0.6 \]
Therefore, the z-score corresponding to a sample mean of 6.5 is 0.6. Since a z-score of 0.6 is not significantly high or low (it is within the range of -2 to 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F899c9d7f-c405-4c72-8a00-0f711d96c18e%2Fbd738804-580c-45eb-9700-4c17a48ddfe5%2Fjadvf6p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Z-Scores and Sample Means**
According to the Official Stage Magician Handbook, magic rabbit weight (in pounds) is normally distributed with a mean (μ) of 6.2 and a standard deviation (σ) of 1.5.
Consider obtaining a random sample of 9 magic rabbits.
**Question:**
Would it be unusual for the sample mean to be at least 6.5? Why or why not?
**Choices:**
1. No, because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.
2. Yes, because the z-score corresponding to a sample mean of 6.5 would be z = 0.60.
3. No, because the z-score corresponding to a sample mean of 6.5 would be z = 0.60.
4. Yes, because the z-score corresponding to a sample mean of 6.5 would be z = 0.20.
**Explanation:**
- **Mean (μ):** 6.2
- **Standard Deviation (σ):** 1.5
- **Sample Size (n):** 9
- **Sample Mean (X̄):** 6.5
To determine if it is unusual for the sample mean to be at least 6.5, we need to calculate the z-score. The formula for the z-score for a sample mean is:
\[ z = \frac{X̄ - μ}{\frac{σ}{\sqrt{n}}} \]
Given the values:
\[ z = \frac{6.5 - 6.2}{\frac{1.5}{\sqrt{9}}} \]
First, calculate the standard error (SE):
\[ SE = \frac{σ}{\sqrt{n}} = \frac{1.5}{\sqrt{9}} = \frac{1.5}{3} = 0.5 \]
Now, calculate the z-score:
\[ z = \frac{6.5 - 6.2}{0.5} = \frac{0.3}{0.5} = 0.6 \]
Therefore, the z-score corresponding to a sample mean of 6.5 is 0.6. Since a z-score of 0.6 is not significantly high or low (it is within the range of -2 to 2
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