Flights approaching major airports in the US during peak hours often experience delays in landing due to air traffic congestion. You will often hear announcements from the pilot that sound like this - “… we expect to land at 5:25PM subject to air traffic delays”. Assume that flights flying in to an airport during peak hours are subject to delays that are uniformly distributed between 10 and 45 minutes. [Be sure to show your calculations for parts (b) through (f).] a. Draw the probability distribution of air traffic delay. b. What is the probability that a flight will have an air traffic delay of less than 9 minutes? c. What is the expected value of air traffic delay? d. What is the standard deviation of air traffic delay?
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Flights approaching major airports in the US during peak hours often experience
delays in landing due to air traffic congestion. You will often hear announcements from the
pilot that sound like this - “… we expect to land at 5:25PM subject to air traffic delays”.
Assume that flights flying in to an airport during peak hours are subject to delays that are
uniformly distributed between 10 and 45 minutes. [Be sure to show your calculations for
parts (b) through (f).]
a. Draw the probability distribution of air traffic delay.
b. What is the probability that a flight will have an air traffic delay of less than 9
minutes?
c. What is the expected value of air traffic delay?
d. What is the standard deviation of air traffic delay?
e. What is the probability that a flight will be delayed between 30 and 40 minutes?
f. What is the probability a flight will be delayed more than 50 minutes?
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