A certain airline sometimes overbooks flights for one of its small aircraft. For a randomly selected flight, let X represent the seating situation (1= overbook by one, 0=full and -1=empty seat). The probability distribution for X is:x-101p(x).15.65.20a) Find the meanb)The flight leaves on time if it is not overbooked. What is the probability the next flight leaves on time?c)Find the expected value for this airline's seating situationd)How many standard deviations from the mean is the overbooked by one (x=1) situation? Hint SD(x)=.59

a) The mean is calculated as: EX=∑xxpx=-1×0.15+0×0.65+1×0.20=-0.15+0+0.20=0.05 Hence, the mean is…

Answered: A certain airline sometimes overbooks…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Question

A certain airline sometimes overbooks flights for one of its small aircraft. For a randomly selected flight, let X represent the seating situation (1= overbook by one, 0=full and -1=empty seat). The probability distribution for X is:

x	-1	0	1
p(x)	.15	.65	.20

a) Find the mean

b)The flight leaves on time if it is not overbooked. What is the probability the next flight leaves on time?

c)Find the expected value for this airline's seating situation

d)How many standard deviations from the mean is the overbooked by one (x=1) situation? Hint SD(x)=.59

Expert Solution

Step 1

a) The mean is calculated as:

$\begin{array}{rcl} E (X) & = & \sum_{x} x p (x) \\ = & (- 1 \times 0.15) + (0 \times 0.65) + (1 \times 0.20) \\ = & - 0.15 + 0 + 0.20 \\ = & 0.05 \end{array}$