(a) Show the graph of the probability density function for flight time. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 230 on the horizontal axis. A 1/20 unit long vertical line segment begins at 250 on the horizontal axis. A 20 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 230 on the horizontal axis. A 1/20 unit long vertical line segment begins at 260 on the horizontal axis. A 30 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 240 on the horizontal axis. A 1/20 unit long vertical line segment begins at 250 on the horizontal axis. A 10 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 240 on the horizontal axis. A 1/20 unit long vertical line segment begins at 260 on the horizontal axis. A 20 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. (b) What is the probability that the flight will be no more than 5 minutes late? (c) What is the probability that the flight will be more than 10 minutes late? (d) What is the expected flight time, in minutes?

(a) Show the graph of the probability density function for flight time. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 230 on the horizontal axis. A 1/20 unit long vertical line segment begins at 250 on the horizontal axis. A 20 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 230 on the horizontal axis. A 1/20 unit long vertical line segment begins at 260 on the horizontal axis. A 30 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 240 on the horizontal axis. A 1/20 unit long vertical line segment begins at 250 on the horizontal axis. A 10 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/20 unit long vertical line segment begins at 240 on the horizontal axis. A 1/20 unit long vertical line segment begins at 260 on the horizontal axis. A 20 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments. (b) What is the probability that the flight will be no more than 5 minutes late? (c) What is the probability that the flight will be more than 10 minutes late? (d) What is the expected flight time, in minutes?

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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Question

Delta Airlines quotes a flight time of 4 hours, 5 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 4 hours and 4 hours, 20 minutes.

(a)

Show the graph of the probability density function for flight time.

The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 230, 240, 250, 260. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/20, 1/10, 3/20. The shaded area is the region bounded by the horizontal axis and the following line segments.

A 1/20 unit long vertical line segment begins at 230 on the horizontal axis.
A 1/20 unit long vertical line segment begins at 250 on the horizontal axis.
A 20 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments.

A 1/20 unit long vertical line segment begins at 230 on the horizontal axis.
A 1/20 unit long vertical line segment begins at 260 on the horizontal axis.
A 30 unit long horizontal line segment begins at the tickmark labeled 230 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments.

A 1/20 unit long vertical line segment begins at 240 on the horizontal axis.
A 1/20 unit long vertical line segment begins at 250 on the horizontal axis.
A 10 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments.

A 1/20 unit long vertical line segment begins at 240 on the horizontal axis.
A 1/20 unit long vertical line segment begins at 260 on the horizontal axis.
A 20 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/20 on the vertical axis. This line segment connects the two vertical line segments.

(b)

What is the probability that the flight will be no more than 5 minutes late?

(c)

What is the probability that the flight will be more than 10 minutes late?

(d)

What is the expected flight time, in minutes?

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