Question

Delta Airlines quotes a flight time of 3 hours, 5 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 3 hours and 3 hours, 40 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: 170, 180, 190, 200, 210, 220. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/40, 1/20, 3/40. The shaded area is the region bounded by the horizontal axis and the following line segments.

• A 1/40 unit long vertical line segment begins at 170 on the horizontal axis.
• A 1/40 unit long vertical line segment begins at 210 on the horizontal axis.
• A 40 unit long horizontal line segment begins at the tickmark labeled 170 on the horizontal axis and the tickmark labeled 1/40 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: 170, 180, 190, 200, 210, 220. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/40, 1/20, 3/40. The shaded area is the region bounded by the horizontal axis and the following line segments.

• A 1/40 unit long vertical line segment begins at 170 on the horizontal axis.
• A 1/40 unit long vertical line segment begins at 220 on the horizontal axis.
• A 50 unit long horizontal line segment begins at the tickmark labeled 170 on the horizontal axis and the tickmark labeled 1/40 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: 170, 180, 190, 200, 210, 220. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/40, 1/20, 3/40. The shaded area is the region bounded by the horizontal axis and the following line segments.

• A 1/40 unit long vertical line segment begins at 180 on the horizontal axis.
• A 1/40 unit long vertical line segment begins at 220 on the horizontal axis.
• A 40 unit long horizontal line segment begins at the tickmark labeled 180 on the horizontal axis and the tickmark labeled 1/40 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: 170, 180, 190, 200, 210, 220. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/40, 1/20, 3/40. The shaded area is the region bounded by the horizontal axis and the following line segments.

• A 1/40 unit long vertical line segment begins at 180 on the horizontal axis.
• A 1/40 unit long vertical line segment begins at 210 on the horizontal axis.
• A 30 unit long horizontal line segment begins at the tickmark labeled 180 on the horizontal axis and the tickmark labeled 1/40 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?

min

Answer 1

a) 3rd plot is correct : limits from 180 to 220

b)

probability that the flight will be no more than 5 minutes late: P(X<10) =10/40 =0.25

c)

probability that the flight will be more than 10 minutes late =P(X>15)=(40-15)/40=0.625

d)

expected flight time, in minutes =(a+b)/2 =(180+220)/2 =200 minutes