b. Find the mean and standard deviation of x. (Round to three decimal places as needed.) II
b. Find the mean and standard deviation of x. (Round to three decimal places as needed.) II
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Solve question b
![**Title: Uniform Probability Distribution**
**Problem Statement:**
Suppose \( x \) is a random variable best described by a uniform probability distribution with \( c = 35 \) and \( d = 65 \).
**Tasks:**
a. **Find \( f(x) \).**
b. **Find the mean and standard deviation of \( x \).**
c. **Graph \( f(x) \) and locate \( \mu \) and the interval \( \mu \pm 2\sigma \) on the graph.** Note that the probability that \( x \) assumes a value within the interval \( \mu \pm 2\sigma \) is equal to 1.
---
**Solutions:**
**a. Find \( f(x) \). Choose the correct answer below:**
- **A.** \( f(x) = \frac{1}{35} \) for \( 65 \leq x \)
- **B.** \( f(x) = \frac{1}{35} \) for \( 0 \leq x \leq 65 \)
- **C.** \( f(x) = \frac{1}{30} \) for \( 35 \leq x \leq 65 \) *(Selected Answer)*
- **D.** \( f(x) = \frac{1}{30} \) for \( 35 \leq x \)
**b. Find the mean and standard deviation of \( x \).**
- \( \mu = \) [Text Box]
- \( \sigma = \) [Text Box]
*(Round to three decimal places as needed.)*
**c. Graph \( f(x) \) and label \( \mu \) and the interval \( \mu \pm 2\sigma \) on the graph. Choose the correct graph below:**
**Graph Options:**
- **A.** Displays a uniform distribution from 35 to 65 with a probability height of \(\frac{1}{30}\). The graph spans the interval and marks the mean \( \mu \) at the center, with the range \( \mu \pm 2\sigma \) indicated on the x-axis.
- **B.** Incorrect range and probability height.
- **C.** Incorrect placement of \( \mu \) and \( \mu \pm 2\sigma \).
*(Option A is the correct](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6420665c-36d2-4993-9fc1-2eb7fb60dd8b%2F4be2572e-61b2-44a2-86ad-c9e422803eb1%2Fo82rqw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Uniform Probability Distribution**
**Problem Statement:**
Suppose \( x \) is a random variable best described by a uniform probability distribution with \( c = 35 \) and \( d = 65 \).
**Tasks:**
a. **Find \( f(x) \).**
b. **Find the mean and standard deviation of \( x \).**
c. **Graph \( f(x) \) and locate \( \mu \) and the interval \( \mu \pm 2\sigma \) on the graph.** Note that the probability that \( x \) assumes a value within the interval \( \mu \pm 2\sigma \) is equal to 1.
---
**Solutions:**
**a. Find \( f(x) \). Choose the correct answer below:**
- **A.** \( f(x) = \frac{1}{35} \) for \( 65 \leq x \)
- **B.** \( f(x) = \frac{1}{35} \) for \( 0 \leq x \leq 65 \)
- **C.** \( f(x) = \frac{1}{30} \) for \( 35 \leq x \leq 65 \) *(Selected Answer)*
- **D.** \( f(x) = \frac{1}{30} \) for \( 35 \leq x \)
**b. Find the mean and standard deviation of \( x \).**
- \( \mu = \) [Text Box]
- \( \sigma = \) [Text Box]
*(Round to three decimal places as needed.)*
**c. Graph \( f(x) \) and label \( \mu \) and the interval \( \mu \pm 2\sigma \) on the graph. Choose the correct graph below:**
**Graph Options:**
- **A.** Displays a uniform distribution from 35 to 65 with a probability height of \(\frac{1}{30}\). The graph spans the interval and marks the mean \( \mu \) at the center, with the range \( \mu \pm 2\sigma \) indicated on the x-axis.
- **B.** Incorrect range and probability height.
- **C.** Incorrect placement of \( \mu \) and \( \mu \pm 2\sigma \).
*(Option A is the correct
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