Determine Px and o from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate. μ=56, o = 12, n = 15 ORCH CHUN = 0.800 4 OA. H = 56,0 OB. H=56, o = 3.098 C. Hx = 56,0 = 12 O D. H=32.332, o = 3.098
Determine Px and o from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate. μ=56, o = 12, n = 15 ORCH CHUN = 0.800 4 OA. H = 56,0 OB. H=56, o = 3.098 C. Hx = 56,0 = 12 O D. H=32.332, o = 3.098
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Determining the Parameters of Population and Sample Size
#### Given Data:
- Population Mean (μ): 56
- Population Standard Deviation (σ): 12
- Sample Size (n): 15
#### Task:
Determine the sample mean (\(\mu_x\)) and the sample standard deviation (\(\sigma_x\)) from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate.
#### Options:
- **A.** \(\mu_x = 56, \sigma_x = 0.800\)
- **B.** \(\mu_x = 56, \sigma_x = 3.098\)
- **C.** \(\mu_x = 56, \sigma_x = 12\)
- **D.** \(\mu_x = 32.332, \sigma_x = 3.098\)
### Explanation:
To solve this, let’s review the formulas used to determine \(\mu_x\) and \(\sigma_x\):
1. **Sample Mean (\(\mu_x\)):** This is usually equal to the population mean (μ).
\[
\mu_x = \mu
\]
Therefore,
\[
\mu_x = 56
\]
2. **Sample Standard Deviation (\(\sigma_x\)):** This can be calculated using the formula:
\[
\sigma_x = \frac{\sigma}{\sqrt{n}}
\]
Where:
- \(\sigma\) is the population standard deviation
- \(n\) is the sample size
Substituting the given values:
\[
\sigma_x = \frac{12}{\sqrt{15}}
\]
Calculate the square root of the sample size:
\[
\sqrt{15} \approx 3.873
\]
Then,
\[
\sigma_x = \frac{12}{3.873} \approx 3.098
\]
Thus, the correct values are:
\[
\mu_x = 56 \quad \text{and} \quad \sigma_x \approx 3.098
\]
### Correct Answer:
**B. \(\mu_x = 56, \sigma_x = 3.098\)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9915ac65-dbee-4978-ab2b-245d47847728%2F2363cdd0-1c58-4ddd-8293-652520e17408%2Ffvahlxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Parameters of Population and Sample Size
#### Given Data:
- Population Mean (μ): 56
- Population Standard Deviation (σ): 12
- Sample Size (n): 15
#### Task:
Determine the sample mean (\(\mu_x\)) and the sample standard deviation (\(\sigma_x\)) from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate.
#### Options:
- **A.** \(\mu_x = 56, \sigma_x = 0.800\)
- **B.** \(\mu_x = 56, \sigma_x = 3.098\)
- **C.** \(\mu_x = 56, \sigma_x = 12\)
- **D.** \(\mu_x = 32.332, \sigma_x = 3.098\)
### Explanation:
To solve this, let’s review the formulas used to determine \(\mu_x\) and \(\sigma_x\):
1. **Sample Mean (\(\mu_x\)):** This is usually equal to the population mean (μ).
\[
\mu_x = \mu
\]
Therefore,
\[
\mu_x = 56
\]
2. **Sample Standard Deviation (\(\sigma_x\)):** This can be calculated using the formula:
\[
\sigma_x = \frac{\sigma}{\sqrt{n}}
\]
Where:
- \(\sigma\) is the population standard deviation
- \(n\) is the sample size
Substituting the given values:
\[
\sigma_x = \frac{12}{\sqrt{15}}
\]
Calculate the square root of the sample size:
\[
\sqrt{15} \approx 3.873
\]
Then,
\[
\sigma_x = \frac{12}{3.873} \approx 3.098
\]
Thus, the correct values are:
\[
\mu_x = 56 \quad \text{and} \quad \sigma_x \approx 3.098
\]
### Correct Answer:
**B. \(\mu_x = 56, \sigma_x = 3.098\)**
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