SAT Writing scores are distributed in population with μ = 487 and a = 115. Describe the sampling distribution of sample mean (the shape, mean, and standard error) for n = 64. p Normal; 487; 14.38 Normal; 487; 115 Normal; 487; 1.80 Uniform; 487; 115
SAT Writing scores are distributed in population with μ = 487 and a = 115. Describe the sampling distribution of sample mean (the shape, mean, and standard error) for n = 64. p Normal; 487; 14.38 Normal; 487; 115 Normal; 487; 1.80 Uniform; 487; 115
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
Question
![### Understanding the Sampling Distribution of SAT Writing Scores
SAT Writing scores are distributed in the population with a mean (µ) of 487 and a standard deviation (σ) of 115. The task involves describing the sampling distribution of the sample mean (including the shape, mean, and standard error) for a sample size (n) of 64.
#### Key Concepts:
- **Population Mean (µ)**: 487
- **Population Standard Deviation (σ)**: 115
- **Sample Size (n)**: 64
The possible answers for the sampling distribution of the sample mean are provided as:
1. **Normal; 487; 14.38**
2. **Normal; 487; 115**
3. **Normal; 487; 1.80**
4. **Uniform; 487; 115**
#### Explanation:
- The shape of the sampling distribution of the sample mean for large samples (according to the Central Limit Theorem) will approximate a normal distribution regardless of the population distribution.
- The mean of the sampling distribution of the sample mean is equal to the population mean (µ = 487).
- The standard error of the mean (σx̄) is calculated using the formula:
\[
\sigma_{x̄} = \frac{\sigma}{\sqrt{n}}
\]
For our example:
\[
\sigma_{x̄} = \frac{115}{\sqrt{64}} = \frac{115}{8} = 14.38
\]
#### Correct Answer:
The correct description of the sampling distribution is:
- **Normal; 487; 14.38**
This means, with a sample size of 64, the distribution of the sample mean SAT Writing scores is normally distributed with a mean of 487 and a standard error of 14.38.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a520971-fd90-49dd-bfdc-9027208d76cd%2Ff30857b3-22c7-4d13-a8d5-9d45a771a2c8%2Fein4k7y_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Sampling Distribution of SAT Writing Scores
SAT Writing scores are distributed in the population with a mean (µ) of 487 and a standard deviation (σ) of 115. The task involves describing the sampling distribution of the sample mean (including the shape, mean, and standard error) for a sample size (n) of 64.
#### Key Concepts:
- **Population Mean (µ)**: 487
- **Population Standard Deviation (σ)**: 115
- **Sample Size (n)**: 64
The possible answers for the sampling distribution of the sample mean are provided as:
1. **Normal; 487; 14.38**
2. **Normal; 487; 115**
3. **Normal; 487; 1.80**
4. **Uniform; 487; 115**
#### Explanation:
- The shape of the sampling distribution of the sample mean for large samples (according to the Central Limit Theorem) will approximate a normal distribution regardless of the population distribution.
- The mean of the sampling distribution of the sample mean is equal to the population mean (µ = 487).
- The standard error of the mean (σx̄) is calculated using the formula:
\[
\sigma_{x̄} = \frac{\sigma}{\sqrt{n}}
\]
For our example:
\[
\sigma_{x̄} = \frac{115}{\sqrt{64}} = \frac{115}{8} = 14.38
\]
#### Correct Answer:
The correct description of the sampling distribution is:
- **Normal; 487; 14.38**
This means, with a sample size of 64, the distribution of the sample mean SAT Writing scores is normally distributed with a mean of 487 and a standard error of 14.38.
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 3 steps with 4 images
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