A population has parameters u = 70.7 and o = 61. You intend to draw a random sample of size n = 146. 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 u = 70.7 and o = 61. You intend to draw a random sample of size n = 146. 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 First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Topic Video
Question
Urgent need help immediately
![**Understanding the Distribution of Sample Means**
Let's start with a given population that parameters specified. Here are the details:
- The population mean (μ) is 70.7.
- The population standard deviation (σ) is 61.
- We intend to draw a random sample of size n = 146.
We need to determine two key characteristics of the distribution of sample means:
1. **Mean of the Distribution of Sample Means (μₓ̅):**
The mean of the distribution of sample means is the same as the population mean (μ). Hence:
\[ \mu_{x̄} = \mu = 70.7 \]
2. **Standard Deviation of the Distribution of Sample Means (σₓ̅):**
The standard deviation of the distribution of sample means (also known as the standard error) can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). This is given by the formula:
\[ \sigma_{x̄} = \frac{\sigma}{\sqrt{n}} \]
Plugging in the values:
\[ \sigma_{x̄} = \frac{61}{\sqrt{146}} \approx \frac{61}{12.08} \approx 5.05 \]
Remember to report the answer accurate to 2 decimal places:
\[ \sigma_{x̄} = 5.05 \]
In summary:
- The mean of the distribution of sample means (μₓ̅) is 70.7.
- The standard deviation of the distribution of sample means (σₓ̅) is 5.05.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F828fe599-f033-4e13-bbc5-938fe3ceb9f0%2F06d916ca-9191-4d61-ac2a-f1c5b564bac9%2Fvuqotw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Distribution of Sample Means**
Let's start with a given population that parameters specified. Here are the details:
- The population mean (μ) is 70.7.
- The population standard deviation (σ) is 61.
- We intend to draw a random sample of size n = 146.
We need to determine two key characteristics of the distribution of sample means:
1. **Mean of the Distribution of Sample Means (μₓ̅):**
The mean of the distribution of sample means is the same as the population mean (μ). Hence:
\[ \mu_{x̄} = \mu = 70.7 \]
2. **Standard Deviation of the Distribution of Sample Means (σₓ̅):**
The standard deviation of the distribution of sample means (also known as the standard error) can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). This is given by the formula:
\[ \sigma_{x̄} = \frac{\sigma}{\sqrt{n}} \]
Plugging in the values:
\[ \sigma_{x̄} = \frac{61}{\sqrt{146}} \approx \frac{61}{12.08} \approx 5.05 \]
Remember to report the answer accurate to 2 decimal places:
\[ \sigma_{x̄} = 5.05 \]
In summary:
- The mean of the distribution of sample means (μₓ̅) is 70.7.
- The standard deviation of the distribution of sample means (σₓ̅) is 5.05.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON