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Delta Airlines quotes a flight time of2hours,3minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed...
Delta Airlines quotes a flight time of 2 hours, 3 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 24 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: 114, 120, 126, 132, 138, 144. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/24, 1/12, 1/8. The shaded area is the region bounded by the horizontal axis and the following line segments.
- A 1/24 unit long vertical line segment begins at 114 on the horizontal axis.
- A 1/24 unit long vertical line segment begins at 144 on the horizontal axis.
- A 30 unit long horizontal line segment begins at the tickmark labeled 114 on the horizontal axis and the tickmark labeled 1/24 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: 114, 120, 126, 132, 138, 144. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/24, 1/12, 1/8. The shaded area is the region bounded by the horizontal axis and the following line segments.
- A 1/24 unit long vertical line segment begins at 120 on the horizontal axis.
- A 1/24 unit long vertical line segment begins at 144 on the horizontal axis.
- A 24 unit long horizontal line segment begins at the tickmark labeled 120 on the horizontal axis and the tickmark labeled 1/24 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: 114, 120, 126, 132, 138, 144. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/24, 1/12, 1/8. The shaded area is the region bounded by the horizontal axis and the following line segments.
- A 1/24 unit long vertical line segment begins at 114 on the horizontal axis.
- A 1/24 unit long vertical line segment begins at 138 on the horizontal axis.
- A 24 unit long horizontal line segment begins at the tickmark labeled 114 on the horizontal axis and the tickmark labeled 1/24 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: 114, 120, 126, 132, 138, 144. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/24, 1/12, 1/8. The shaded area is the region bounded by the horizontal axis and the following line segments.
- A 1/24 unit long vertical line segment begins at 120 on the horizontal axis.
- A 1/24 unit long vertical line segment begins at 138 on the horizontal axis.
- A 18 unit long horizontal line segment begins at the tickmark labeled 120 on the horizontal axis and the tickmark labeled 1/24 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 3 minutes late?
(c)
What is the probability that the flight will be more than 6 minutes late?
(d)
What is the expected flight time, in minutes?
min
