Certainly! Here's a transcription for an educational website:---**Determine \(\mu_x\) and \(\sigma_x\) from the given parameters of the population and sample size.**- Population mean (\(\mu\)): 75- Population standard deviation (\(\sigma\)): 28- Sample size (\(n\)): 49\[\mu_x = \, \text{[Blank for students to fill in]}\]---**Explanation:**To calculate the sample mean (\(\mu_x\)) and sample standard deviation (\(\sigma_x\)), use the following formulas:1. **Sample Mean (\(\mu_x\)):** For the sample mean, it remains the same as the population mean. \[ \mu_x = \mu = 75 \]2. **Sample Standard Deviation (\(\sigma_x\)):** This is calculated using the formula: \[ \sigma_x = \frac{\sigma}{\sqrt{n}} \] Here, \(\sigma = 28\) and \(n = 49\). So, \(\sigma_x = \frac{28}{\sqrt{49}} = 4\).Students should use these calculations to fill in the blanks and understand the relationship between population parameters and sample statistics.

According to the given information, the random variable X have mean µx = 75 and the standard deviation of σ x = 28.According to central limit theorem, for large sample (>30) or if the population follows normal distribution, then the sampling distribution of the sample mean follows normal distribution with the expectation and standard deviation defined as follows: E(x̅) = µ and SD(x̅) = σ/√n. Here, n is the sample size, µ is the population mean and σ is the population standard deviation of the random variable X. Consider that x̅ is the sample mean. Now, for sample of 49, the mean of the sampling distribution of the sample mean is, µx̅ = 75. Now, for sample of 49, the standard deviation of the sampling distribution of the sample mean is, σx̅ = 28/√49 = 4. Thus, the sampling distribution of x̅ is approximately normal with mean µx̅ = 75 and standard deviation σx̅ = 4.

Answered: Determine u; and o; from the given…

Math

Statistics

Determine u; and o; from the given parameters of the population and sample size. H= 75, o = 28, n= 49

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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