A population has parameters µ = 41 and o = 71.4. You intend to draw a random sample of s n = 174. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
A population has parameters µ = 41 and o = 71.4. You intend to draw a random sample of s n = 174. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 3BGP
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![### Understanding the Distribution of Sample Means
A population has parameters μ = 41 and σ = 71.4. You intend to draw a random sample of size n = 174.
#### Calculation Questions
1. **What is the mean of the distribution of sample means?**
\[ \mu_{\bar{x}} = \]
2. **What is the standard deviation of the distribution of sample means?**
*(Report answer accurate to 2 decimal places.)*
\[ \sigma_{\bar{x}} = \]
### Explanation:
- **Mean of the Distribution of Sample Means (\( \mu_{\bar{x}} \))**: This is the same as the population mean (μ).
- **Standard Deviation of the Distribution of Sample Means (\( \sigma_{\bar{x}} \))**: This is calculated using the population standard deviation (σ) divided by the square root of the sample size (n). The formula is:
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]
For this specific problem, you would plug in the values as follows:
\[ \sigma_{\bar{x}} = \frac{71.4}{\sqrt{174}} \]
Be sure to perform the calculation accurately and round the result to two decimal places as requested.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5da0de8c-ddb4-42a7-a82e-d33a1c834dcf%2F77d1912c-f2dd-48a4-a9f4-14aecf98d785%2F4zgvik7_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Distribution of Sample Means
A population has parameters μ = 41 and σ = 71.4. You intend to draw a random sample of size n = 174.
#### Calculation Questions
1. **What is the mean of the distribution of sample means?**
\[ \mu_{\bar{x}} = \]
2. **What is the standard deviation of the distribution of sample means?**
*(Report answer accurate to 2 decimal places.)*
\[ \sigma_{\bar{x}} = \]
### Explanation:
- **Mean of the Distribution of Sample Means (\( \mu_{\bar{x}} \))**: This is the same as the population mean (μ).
- **Standard Deviation of the Distribution of Sample Means (\( \sigma_{\bar{x}} \))**: This is calculated using the population standard deviation (σ) divided by the square root of the sample size (n). The formula is:
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]
For this specific problem, you would plug in the values as follows:
\[ \sigma_{\bar{x}} = \frac{71.4}{\sqrt{174}} \]
Be sure to perform the calculation accurately and round the result to two decimal places as requested.
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