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The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/20 where x goes between 1 and 21 minutes. Round answers to 4 decimal places when possible. a. This is a Uniform distribution. b. It is a Continuous distribution. c. The mean of this distribution is 11 d. The standard deviation is 5.7735 e. Find the probability that the time will be at most 13 minutes. f. Find the probability that the time will be between 6 and 16 minutes. g. Find the 30th percentile.

The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/20 where x goes between 1 and 21 minutes. Round answers to 4 decimal places when possible. a. This is a Uniform distribution. b. It is a Continuous distribution. c. The mean of this distribution is 11 d. The standard deviation is 5.7735 e. Find the probability that the time will be at most 13 minutes. f. Find the probability that the time will be between 6 and 16 minutes. g. Find the 30th percentile.

MATLAB: An Introduction with Applications
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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**Understanding Uniform Distribution in Train Arrival Times** The time it takes for the next train to arrive follows a uniform distribution, defined by the probability density function \( f(x) = 1/20 \) for times between 1 and 21 minutes. Here, we illustrate some key properties and computations related to this distribution. a. **Type of Distribution:** - This is a **Uniform** distribution. b. **Nature of Distribution:** - It is a **Continuous** distribution. c. **Mean of the Distribution:** - The mean of this distribution is **11**. d. **Standard Deviation:** - The standard deviation is **5.7735**. **Calculations:** e. **Probability of Time ≤ 13 minutes:** - Calculate the probability that the time will be at most 13 minutes. [Answer Box] f. **Probability of Time Between 6 and 16 minutes:** - Calculate the probability that the time will be between 6 and 16 minutes. [Answer Box] g. **30th Percentile:** - Determine the 30th percentile. [Answer Box] h. **Probability of Time > 17 minutes, Given Time ≥ 3 minutes:** - Calculate the conditional probability that the time is more than 17 minutes given it is at least 3 minutes. [Answer Box] These calculations help in understanding how the uniform distribution operates in real-world situations, such as predicting train arrival times.
Transcribed Image Text:**Understanding Uniform Distribution in Train Arrival Times** The time it takes for the next train to arrive follows a uniform distribution, defined by the probability density function \( f(x) = 1/20 \) for times between 1 and 21 minutes. Here, we illustrate some key properties and computations related to this distribution. a. **Type of Distribution:** - This is a **Uniform** distribution. b. **Nature of Distribution:** - It is a **Continuous** distribution. c. **Mean of the Distribution:** - The mean of this distribution is **11**. d. **Standard Deviation:** - The standard deviation is **5.7735**. **Calculations:** e. **Probability of Time ≤ 13 minutes:** - Calculate the probability that the time will be at most 13 minutes. [Answer Box] f. **Probability of Time Between 6 and 16 minutes:** - Calculate the probability that the time will be between 6 and 16 minutes. [Answer Box] g. **30th Percentile:** - Determine the 30th percentile. [Answer Box] h. **Probability of Time > 17 minutes, Given Time ≥ 3 minutes:** - Calculate the conditional probability that the time is more than 17 minutes given it is at least 3 minutes. [Answer Box] These calculations help in understanding how the uniform distribution operates in real-world situations, such as predicting train arrival times.
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