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A population of values has an unknown distribution with = 145.7 and o= 54.4. You intend to draw a random sample of size n = 239. What is the mean of the distribution of sample means? Hz= (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? On= (Please report your answer accurate to 2 decimal places.)

A population of values has an unknown distribution with = 145.7 and o= 54.4. You intend to draw a random sample of size n = 239. What is the mean of the distribution of sample means? Hz= (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? On= (Please report your answer accurate to 2 decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Understanding Distribution of Sample Means A population of values has an unknown distribution with a mean (μ) of 145.7 and a standard deviation (σ) of 54.4. You intend to draw a random sample of size \( n = 239 \). #### What is the mean of the distribution of sample means? \[ μ_x = \] (Please enter an exact answer.) #### What is the standard deviation of the distribution of sample means? \[ σ_x = \] (Please report your answer accurate to 2 decimal places.) --- In this task, you are required to calculate the mean and the standard deviation of the sample means from the given population parameters. - **Mean of Sample Means (μ_x):** The mean of the distribution of sample means is the same as the mean of the population (\( μ \)). - **Standard Deviation of Sample Means (σ_x):** The standard deviation of the sample means is calculated by dividing the population standard deviation (\( σ \)) by the square root of the sample size (\( n \)). The formulas are: \[ μ_x = μ \] \[ σ_x = \frac{σ}{\sqrt{n}} \] To find the exact value of \( μ_x \), input the given value of \( μ \). To find \( σ_x \), compute the square root of the sample size \( n \) and then divide \( σ \) by this value, ensuring your answer is accurate to two decimal places.
Transcribed Image Text:### Understanding Distribution of Sample Means A population of values has an unknown distribution with a mean (μ) of 145.7 and a standard deviation (σ) of 54.4. You intend to draw a random sample of size \( n = 239 \). #### What is the mean of the distribution of sample means? \[ μ_x = \] (Please enter an exact answer.) #### What is the standard deviation of the distribution of sample means? \[ σ_x = \] (Please report your answer accurate to 2 decimal places.) --- In this task, you are required to calculate the mean and the standard deviation of the sample means from the given population parameters. - **Mean of Sample Means (μ_x):** The mean of the distribution of sample means is the same as the mean of the population (\( μ \)). - **Standard Deviation of Sample Means (σ_x):** The standard deviation of the sample means is calculated by dividing the population standard deviation (\( σ \)) by the square root of the sample size (\( n \)). The formulas are: \[ μ_x = μ \] \[ σ_x = \frac{σ}{\sqrt{n}} \] To find the exact value of \( μ_x \), input the given value of \( μ \). To find \( σ_x \), compute the square root of the sample size \( n \) and then divide \( σ \) by this value, ensuring your answer is accurate to two decimal places.
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