### Probability and Population Mean AnalysisThis content discusses the probability of a sample mean and its relationship with the population mean, specifically in relation to measurements in inches.#### Graph ExplanationA bell-shaped curve (normal distribution graph) is provided, showing a range of values from 10 to 34 inches on the x-axis. The peak of the curve suggests the most common value in the data set, with the values tapering off symmetrically on either side, indicating the distribution of the data around the mean.#### Questions and Answers**(b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)****Answer:** [Input needed]**(c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)****Answer:** [Input needed]**(d) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?****Options:**- Part (b), because the standard error is smaller.- **Part (c), because the population standard deviation is smaller.**- Part (b), because the population standard deviation is smaller.- Part (c), because the sample size is larger.**Correct Answer:** Part (c), because the population standard deviation is smaller.**Explanation:** The selected answer suggests that the probability of obtaining a sample mean within 1 inch of the population mean is greater when the population standard deviation is smaller. This is because a smaller standard deviation indicates that the data points are closer to the mean, making it more likely that the sample mean will also be close to the population mean.#### Additional HelpFor further assistance, a "Need Help? Read It" button is provided, likely leading to additional resources or explanations.This exercise appears to be part of a statistics or probability lesson, helping students understand the relationship between sample mean, population mean, standard error, and standard deviation. ### Example of Probabilities in Sampling Distributions: Case Study on Annual Rainfall#### Problem ContextThe state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 34 years of rainfall for California and a sample of 50 years of rainfall for New York has been taken.#### Questions and Solutions**(a) Show the probability distribution of the sample mean annual rainfall for California.**Three graphical probability distributions are provided, each representing different sample means for California and New York:1. The first graph is a normal distribution centered around a mean with units in inches ranging from -2.1 to 2.1.2. The second graph is a normal distribution centered around a mean with units in inches ranging from 19.9 to 24.1.3. The third graph is a normal distribution centered around a mean with units in inches ranging from 39.9 to 44.1.4. The fourth graph, which is selected (indicated by the checkmark), is a normal distribution centered around a mean with units in inches ranging from 10 to 34.**(b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)**The response box is empty, and the answer provided is marked incorrect.**(c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)**The response box is also empty, and the answer provided is marked incorrect.#### Explanation of Graphs1. **First Graph:** - **X-Axis:** Values range from -2.1 to 2.1 inches. - **Y-Axis:** Represents probability density. - **Curve:** Normal distribution indicating sample mean deviation.2. **Second Graph:** - **X-Axis:** Values range from 19.9 to 24.1 inches. - **Y-Axis:** Represents probability density. - **Curve:** Normal distribution representing another sample mean value.3. **Third Graph:** - **X-Axis:** Values range from 39.9 to 44.1 inches. - **Y-Axis:** Represents probability density

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a…

Answered: (b) What is the probability that the…

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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