Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a train. Suppose that the density curve is as pictured below (a uniform distribution). Density 0.05 0. 20 Time (minutes) (a) What is the probability that x is less than 7 min? .35 What is the probability that x is more than 13 min? (b) What is the probability that x is between 5 and 9 min? (c) Find the value c (in minutes) for which P(x < c) = 0.7.
Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a train. Suppose that the density curve is as pictured below (a uniform distribution). Density 0.05 0. 20 Time (minutes) (a) What is the probability that x is less than 7 min? .35 What is the probability that x is more than 13 min? (b) What is the probability that x is between 5 and 9 min? (c) Find the value c (in minutes) for which P(x < c) = 0.7.
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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![**Title: Understanding Uniform Distribution in Waiting Times**
**Introduction:**
Let \( x \) represent the amount of time (in minutes) that a particular San Francisco commuter must wait for a train. The density curve below illustrates a uniform distribution.
**Graph Explanation:**
- **Axes:**
- The horizontal axis represents the "Time (minutes)," spanning from 0 to 20.
- The vertical axis represents the "Density," with a constant value of 0.05 across the time interval.
- **Density Curve:**
- The curve is a horizontal line at a density of 0.05 from 0 to 20 minutes, indicating a uniform distribution where each minute is equally likely within this range.
**Probability Questions:**
(a) **Probability that \( x \) is less than 7 minutes:**
\[
\text{Probability} = 0.35
\]
(b) **Probability that \( x \) is more than 13 minutes:**
\[
\text{To be calculated}
\]
(c) **Probability that \( x \) is between 5 and 9 minutes:**
\[
\text{To be calculated}
\]
**Solution Example:**
(c) **Finding the value \( c \) (in minutes) for which \( P(x < c) = 0.7 \):**
\[
c = 14 \text{ minutes}
\]
Understanding this concept allows for the analysis of waiting times and helps in statistics and data analysis by applying the principles of probability using uniform distributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2eaed2be-574b-4250-b175-30e358efe567%2F86dd4341-2a4a-4970-9044-52a181fe20a6%2Ff0x52c7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Uniform Distribution in Waiting Times**
**Introduction:**
Let \( x \) represent the amount of time (in minutes) that a particular San Francisco commuter must wait for a train. The density curve below illustrates a uniform distribution.
**Graph Explanation:**
- **Axes:**
- The horizontal axis represents the "Time (minutes)," spanning from 0 to 20.
- The vertical axis represents the "Density," with a constant value of 0.05 across the time interval.
- **Density Curve:**
- The curve is a horizontal line at a density of 0.05 from 0 to 20 minutes, indicating a uniform distribution where each minute is equally likely within this range.
**Probability Questions:**
(a) **Probability that \( x \) is less than 7 minutes:**
\[
\text{Probability} = 0.35
\]
(b) **Probability that \( x \) is more than 13 minutes:**
\[
\text{To be calculated}
\]
(c) **Probability that \( x \) is between 5 and 9 minutes:**
\[
\text{To be calculated}
\]
**Solution Example:**
(c) **Finding the value \( c \) (in minutes) for which \( P(x < c) = 0.7 \):**
\[
c = 14 \text{ minutes}
\]
Understanding this concept allows for the analysis of waiting times and helps in statistics and data analysis by applying the principles of probability using uniform distributions.
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