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2. 0.15+ 0.1- 0.05- 110 120 130 140 Minutes

2. 0.15+ 0.1- 0.05- 110 120 130 140 Minutes

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. a. Which of the following graphs accurately represents the probability density function for flight time in minutes? 1. \(f(x)\) 0.15
Transcribed Image Text:Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. a. Which of the following graphs accurately represents the probability density function for flight time in minutes? 1. \(f(x)\) 0.15
### Probability Distribution Functions #### Graph 1: - **Type:** Uniform Probability Distribution - **Interval:** 120 to 140 minutes - **Height (f(x)):** 0.05 - **x-axis:** Minutes - **y-axis:** Probability Density (f(x)) - This function represents a uniform probability where any time between 120 and 140 minutes is equally likely. #### Graph 2: - **Type:** Uniform Probability Distribution - **Interval:** 110 to 140 minutes - **Height (f(x)):** Approximately 0.033 - **x-axis:** Minutes - **y-axis:** Probability Density (f(x)) - This depicts a wider uniform distribution from 110 to 140 minutes with a correspondingly lower height since the probability is spread over a longer interval. #### Graph 3: - **Type:** Uniform Probability Distribution - **Interval:** 130 to 140 minutes - **Height (f(x)):** 0.1 - **x-axis:** Minutes - **y-axis:** Probability Density (f(x)) - This represents a distribution focusing on a shorter interval of time from 130 to 140 minutes. ### Questions **b.** What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? **c.** What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? **d.** What is the expected flight time, in minutes? Use these graphs and questions to explore concepts of probability density, uniform distributions, and expected values.
Transcribed Image Text:### Probability Distribution Functions #### Graph 1: - **Type:** Uniform Probability Distribution - **Interval:** 120 to 140 minutes - **Height (f(x)):** 0.05 - **x-axis:** Minutes - **y-axis:** Probability Density (f(x)) - This function represents a uniform probability where any time between 120 and 140 minutes is equally likely. #### Graph 2: - **Type:** Uniform Probability Distribution - **Interval:** 110 to 140 minutes - **Height (f(x)):** Approximately 0.033 - **x-axis:** Minutes - **y-axis:** Probability Density (f(x)) - This depicts a wider uniform distribution from 110 to 140 minutes with a correspondingly lower height since the probability is spread over a longer interval. #### Graph 3: - **Type:** Uniform Probability Distribution - **Interval:** 130 to 140 minutes - **Height (f(x)):** 0.1 - **x-axis:** Minutes - **y-axis:** Probability Density (f(x)) - This represents a distribution focusing on a shorter interval of time from 130 to 140 minutes. ### Questions **b.** What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? **c.** What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? **d.** What is the expected flight time, in minutes? Use these graphs and questions to explore concepts of probability density, uniform distributions, and expected values.
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DISCLAIMER “Since you have asked multiple subparts questions, we will solve the first 3 sub-part question for you as per guidelines If you want any specific question to be solved then please specify the question number or post only that question.”

 

In the question, actual flight times are uniformly divided into 2 hours and 2 hours 20 minutes

Assume X is the flight time

here, X~U (120 min., 140 min.)

The probability density function is

fx=1b-a=1140-120=120,=120<x<140The cumulative distrubution function is,PX≤x=x-ab-a=x-120140-120

 

 

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