The living spaces of all homes in a city have a mean of 2150 square feet and a standard deviation of 400 square feet. Let x be the mean living space for a random sample of 50 homes selected from this city. Find the mean of the sampling distribution of x. Enter an exact answer. mean of x = i Find the standard deviation of the sampling distribution of . Round your answer to one decimal place. square feet standard deviation of x = i square feet
The living spaces of all homes in a city have a mean of 2150 square feet and a standard deviation of 400 square feet. Let x be the mean living space for a random sample of 50 homes selected from this city. Find the mean of the sampling distribution of x. Enter an exact answer. mean of x = i Find the standard deviation of the sampling distribution of . Round your answer to one decimal place. square feet standard deviation of x = i square feet
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![### Understanding the Sampling Distribution
The problem involves calculating the mean and standard deviation of the sampling distribution for the mean living space of homes in a city.
The city homes have:
- **Mean living space**: 2150 square feet
- **Standard deviation**: 400 square feet
A random sample of 50 homes is selected. We need to find the following:
#### 1. Mean of the Sampling Distribution of \(\bar{x}\)
The mean of the sampling distribution of the sample mean (\(\bar{x}\)) is the same as the mean of the population. Therefore:
- **Mean of \(\bar{x}\) = 2150 square feet**
#### 2. Standard Deviation of the Sampling Distribution of \(\bar{x}\)
The standard deviation of the sampling distribution, also known as the standard error, is calculated using the formula:
\[
\text{Standard deviation of } \bar{x} = \frac{\sigma}{\sqrt{n}}
\]
Where:
- \(\sigma\) is the population standard deviation (400 square feet)
- \(n\) is the sample size (50 homes)
Calculate the standard deviation:
\[
\text{Standard deviation of } \bar{x} = \frac{400}{\sqrt{50}} \approx 56.6 \text{ square feet}
\]
**Note**: Round the answer to one decimal place.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27c44973-b695-4838-95b3-ee2a1d975c6e%2F45c06304-e835-46d4-8664-e731c66b60b9%2Fevh87hu_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Sampling Distribution
The problem involves calculating the mean and standard deviation of the sampling distribution for the mean living space of homes in a city.
The city homes have:
- **Mean living space**: 2150 square feet
- **Standard deviation**: 400 square feet
A random sample of 50 homes is selected. We need to find the following:
#### 1. Mean of the Sampling Distribution of \(\bar{x}\)
The mean of the sampling distribution of the sample mean (\(\bar{x}\)) is the same as the mean of the population. Therefore:
- **Mean of \(\bar{x}\) = 2150 square feet**
#### 2. Standard Deviation of the Sampling Distribution of \(\bar{x}\)
The standard deviation of the sampling distribution, also known as the standard error, is calculated using the formula:
\[
\text{Standard deviation of } \bar{x} = \frac{\sigma}{\sqrt{n}}
\]
Where:
- \(\sigma\) is the population standard deviation (400 square feet)
- \(n\) is the sample size (50 homes)
Calculate the standard deviation:
\[
\text{Standard deviation of } \bar{x} = \frac{400}{\sqrt{50}} \approx 56.6 \text{ square feet}
\]
**Note**: Round the answer to one decimal place.
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