### Sampling Distribution of the Sample Mean#### Analyze the Given FigureThe image shows a normal distribution curve representing the sampling distribution of the sample mean. The x-axis is labeled $X$ and ranges from 55 to 145 in increments of 15 units. The curve is symmetric, centered at 100, indicating that the mean ($ \mu_{\bar{x}} $) of the sampling distribution is 100.#### Questions and Explanations(a) What is the value of $ \mu_{\bar{x}} $ ?*Answer: [100]* - **Explanation**: The mean of the sampling distribution of the sample mean ($ \mu_{\bar{x}} $) is the same as the population mean. From the figure, it is evident that the distribution is centered at 100, so $ \mu_{\bar{x}} = 100.**(b) What is the value of \( \sigma_{\bar{x}} $ ?*Answer: [To be determined]* - **Explanation**: The standard deviation of the sampling distribution of the sample mean ($ \sigma_{\bar{x}} $) needs to be calculated. From the graph, we can estimate $ \sigma_{\bar{x}} $ using other given information or required parameters.**(c) If the sample size is $n = 25$, what is the standard deviation of the population from which the sample was drawn?*Answer: [To be determined]* - **Explanation**: To find the standard deviation of the population ($ \sigma $), use the formula connecting the standard deviation of the sample mean ($ \sigma_{\bar{x}} $) and the standard deviation of the population ($ \sigma $):** \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] Given $n = 25$, rearrange the formula to solve for $ \sigma $: \[ \sigma = \sigma_{\bar{x}} \times \sqrt{25} = \sigma_{\bar{x}} \times 5 \] Thus, we need to know $ \sigma_{\bar{x}} $ from part (b) to determine $ \sigma $.### Diagram DetailsThe graph is a typical normal distribution bell curve, symmetrically centered at the mean (100). The labels on the graph (55, 70,

From the figure of the sampling distribution of the sample mean, the middle value is observed to be…

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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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Answer the following questions for the sampling distribution of the sample mean shown in the figure. (a) What is the value of = ? (b) What is the value of 55 70 85 100 115 130 145 X (c) If the sample size is n = 25, what is the standard deviation of the population from which the sample was drawn?