Use the probability distribution for the random variable x to answer the question. 1 2 3 4 p(x) | 0.03 0.2 0.19 0.17 0.35 0.06 Locate the interval u ± 20 on the x-axis of a probability histogram. You are given that the mean is 2.79 and the standard deviation is 1.34. What is the probability that x will fall into this interval?
Use the probability distribution for the random variable x to answer the question. 1 2 3 4 p(x) | 0.03 0.2 0.19 0.17 0.35 0.06 Locate the interval u ± 20 on the x-axis of a probability histogram. You are given that the mean is 2.79 and the standard deviation is 1.34. What is the probability that x will fall into this interval?
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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![**Probability Distribution for Random Variable \( x \)**
Use the probability distribution for the random variable \( x \) to answer the question.
| \( x \) | 0 | 1 | 2 | 3 | 4 | 5 |
|--------------|------|-----|-----|-----|-----|-----|
| \( p(x) \) | 0.03 | 0.2 | 0.19| 0.17| 0.35| 0.06|
Locate the interval \( \mu \pm 2\sigma \) on the x-axis of a probability histogram. You are given that the mean is \( 2.79 \) and the standard deviation is \( 1.34 \).
**Question:** What is the probability that \( x \) will fall into this interval?
- **Graphs/Diagrams:**
The table represents a probability distribution with:
- \( x \): Possible values of the random variable.
- \( p(x) \): Corresponding probabilities for each value of \( x \).
**Additional Notes:**
Calculate the interval \( \mu \pm 2\sigma \) as follows:
- \( \mu - 2\sigma = 2.79 - (2 \times 1.34) \)
- \( \mu + 2\sigma = 2.79 + (2 \times 1.34) \)
Thus, the interval is \( [0.11, 5.47] \).
Identify the probability that \( x \) falls within the interval from the given distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fdf87a1-6c5c-465d-8ddf-eaf69800c0eb%2Fb58ffbfd-679c-4131-9b0f-919c803a7396%2Fpkvij5h_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability Distribution for Random Variable \( x \)**
Use the probability distribution for the random variable \( x \) to answer the question.
| \( x \) | 0 | 1 | 2 | 3 | 4 | 5 |
|--------------|------|-----|-----|-----|-----|-----|
| \( p(x) \) | 0.03 | 0.2 | 0.19| 0.17| 0.35| 0.06|
Locate the interval \( \mu \pm 2\sigma \) on the x-axis of a probability histogram. You are given that the mean is \( 2.79 \) and the standard deviation is \( 1.34 \).
**Question:** What is the probability that \( x \) will fall into this interval?
- **Graphs/Diagrams:**
The table represents a probability distribution with:
- \( x \): Possible values of the random variable.
- \( p(x) \): Corresponding probabilities for each value of \( x \).
**Additional Notes:**
Calculate the interval \( \mu \pm 2\sigma \) as follows:
- \( \mu - 2\sigma = 2.79 - (2 \times 1.34) \)
- \( \mu + 2\sigma = 2.79 + (2 \times 1.34) \)
Thus, the interval is \( [0.11, 5.47] \).
Identify the probability that \( x \) falls within the interval from the given distribution.
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