**Transcription and Explanation for Educational Use**---**Problem Statement 2:**Suppose a random sample of data is taken, sample size \( n = 200 \), with sample mean 100 and sample standard deviation is 10.**a) Calculate the following, giving your answer in interval notation.***For example, \(3 \pm 2\) in interval form would be \((1,5)\) because \(3-2=1\) and \(3+2=5\).*- **Interval 1:** \(\bar{x} \pm s\)- **Interval 2:** \(\bar{x} \pm 2s\)- **Interval 3:** \(\bar{x} \pm 3s\)**Chebychev's Rule****b) Using Chebychev's Inequality**- **AT LEAST** what percentage of data should we expect to be within interval 2?- **AT LEAST** what percentage of data should we expect to be within interval 3? Show your work by using the formula.**Empirical Rule****c) Suppose that the data are sampled from a normally distributed population. Using the empirical rule, what percentage of the data should we expect to be within interval one?**---**Explanation:**1. **Interval Calculations:** - Interval 1 represents the range within one standard deviation from the mean. - Interval 2 represents the range within two standard deviations from the mean. - Interval 3 represents the range within three standard deviations from the mean.2. **Chebychev's Rule:** - This rule provides a minimum percentage of observations that fall within a given number of standard deviations from the mean, applicable to any distribution. - The formula for Chebychev's Inequality is: \( 1 - \frac{1}{k^2} \)3. **Empirical Rule:** - Applicable for normally distributed data, this rule states: - Approximately 68% of data lies within one standard deviation. - Approximately 95% lies within two standard deviations. - Approximately 99.7% lies within three standard deviations.This question requires students to apply statistical concepts, such as interval notation, Chebychev's Inequality, and the Empirical Rule, to estimate data distribution in a sample set.

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Suppose a random sample of data is taken, sample size n = 200, with sample mean 100 and sample standard deviation is 10. ) Calculate the following, giving your answer in interval notation. For example, 3±2 in interval form would be (1,5) because 3-2=1 and 3+2 =5. nterval 1: š ±s nterval 2: š ± 2s nterval 3: š ± 3s

Suppose a random sample of data is taken, sample size n = 200, with sample mean 100 and sample standard deviation is 10. ) Calculate the following, giving your answer in interval notation. For example, 3±2 in interval form would be (1,5) because 3-2=1 and 3+2 =5. nterval 1: š ±s nterval 2: š ± 2s nterval 3: š ± 3s

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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