Certainly! Here's the transcription arranged for an educational website: --- Random Sample Calculation and Chebychev’s Inequality Context: A random sample of data is taken with a sample size $ n = 200 $, a sample mean of 100, and a sample standard deviation of 10. Tasks: 1. Interval Calculations: - Calculate the following, giving your answer in interval notation. - 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 $ 2. Chebychev’s Rule: - b) Using Chebychev’s Inequality - Interval 2: Determine at least what percentage of data should be expected within this interval. - Interval 3: Determine at least what percentage of data should be expected within this interval using the formula. Show your work. 3. Empirical Rule: - c) Normal Distribution Sampling: - Using the empirical rule, determine the percentage of data that should be within interval one. 4. Usefulness of Chebychev’s Inequality: - d) Discussion: Why can't Chebychev’s inequality provide a useful estimate for the percentage of data expected within interval 1? 5. Population Sampling: - e) Normal Distribution: - Assuming the population is normally distributed and the sample size is $ n = 200 $, calculate approximately how many observations should fall within interval 2. Please show your work. --- This transcription provides an overview of statistical concepts like interval calculations, Chebychev’s Inequality, and the empirical rule within a sampling context.

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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Certainly! Here's the transcription arranged for an educational website:

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**Random Sample Calculation and Chebychev’s Inequality**

**Context**: A random sample of data is taken with a sample size $ n = 200 $, a sample mean of 100, and a sample standard deviation of 10.

**Tasks**:

1. **Interval Calculations**:
- Calculate the following, giving your answer in interval notation.
- *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 $

2. **Chebychev’s Rule**:
- **b) Using Chebychev’s Inequality**
- **Interval 2**: Determine *at least* what percentage of data should be expected within this interval.
- **Interval 3**: Determine *at least* what percentage of data should be expected within this interval using the formula. Show your work.

3. **Empirical Rule**:
- **c) Normal Distribution Sampling**:
- Using the empirical rule, determine the percentage of data that should be within interval one.

4. **Usefulness of Chebychev’s Inequality**:
- **d) Discussion**: Why can't Chebychev’s inequality provide a useful estimate for the percentage of data expected within interval 1?

5. **Population Sampling**:
- **e) Normal Distribution**:
- Assuming the population is normally distributed and the sample size is $ n = 200 $, calculate approximately how many observations should fall within interval 2. Please show your work.

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This transcription provides an overview of statistical concepts like interval calculations, Chebychev’s Inequality, and the empirical rule within a sampling context.

Expert Solution

Step 1

Hello there! According to our policies can answer only three sub parts per question. Kindly find the solution to a, b and c. If you have any doubts in remaining parts kindly make a new request mentioning the part which you need help in.

Given
sample size = n = 200
sample mean $\overset{__}{X} = 100$
sample standard deviation $s = 10$

a)
Interval 1 (90,110)
$x - s = 100 - 10 = 90 x + s = 100 + 10 = 110$
Interval 2 (80, 120)
$x - 2 s = 100 - 2 * 10 = 80 x + 2 s = 100 + 2 * 10 = 120$
Interval 3 (70, 130)
$x - 3 s = 100 - 3 * 10 = 70 x + 3 s = 100 + 3 * 10 = 130$