### Understanding the Sampling DistributionThe 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 feetA 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.

given data μ=2150σ=400n=50find the mean of the sampling distribution of x=?

Answered: The living spaces of all homes in a…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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