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Airlines typically accept more reservations for a flight than the number of seats on the plane. Suppose that for a certain route, an airline accepts 40reservations on a plane that carries 38passengers. Based on experience, the probability distribution of Y=the number of passengers who actually show up for a randomly selected flight is given in the following table. You can check that μY=37.4andσY=1.24.

There is also a crew of two flight attendants and two pilots on each flight. Let X=the total number of people (passengers plus crew) on a randomly selected flight.

a. Make a graph of the probability distribution of X. Describe its shape.

b. Find and interpret role="math" μX.

c. Calculate and interpret σX.

Short Answer

Expert verified

a. The distribution is symmetric.

b. μX=41.4

c.σX=1.24

Step by step solution

01

Part(a) Step 1 : Given information

Given table :

02

Part(a) Step 2 : Simplification

Since there are 4crews on each flight, so :

X=Y+4

So, the new table is :

And so, the respective graph is :

The distribution is symmetric.

03

Part(b) Step 1 : Given information

Given table :

04

Part(b) Step 2 : Simplification

Ystands for the number of passengers.

Each flight has four crew members, hence X=Y+4.

When the constant is added to each data value, the distribution's center is also enhanced by that constant value.

μx=μy+4=37.4+5=41.4

When the constant value is added to each data point, the center of the distribution is raised, resulting in 41.4average numbers of persons (passengers + staff) being randomly selected.

05

Part(c) Step 1 : Given information

Given table :

06

Part(c) Step 2 : Simplification

Ystands for the number of passengers.

Because each flight has four crew members, adding the constant to each data value has no effect on the distribution's spread; it remains intact.

1.24=σx=σy

When a constant value is added to each data point, the spread of the distribution is unaffected, and the number of persons (passengers + staff) for a randomly chosen aircraft varies on average 1.24around the mean = 41.4people.

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