Question

On a given Dallas-New York flight, there are 300 seats. Suppose the ticket price is $450 and the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 40 and standard deviation 14. You decide to overbook the flight and estimate that the net cost of an involuntary boarding denial (if the number of passengers exceeds the number of seats) is $900 (everything considered). Suppose you have decided to accept the above optimal number of reservations. Then what is the probability that you won’t need to deal with overbooked passengers?

a. 33%
b. 43%
c. 57%
d. 67%
e. 82%

Answer 1

33% ( A )

Explanation:

Number of seats = 300

Ticket price = $450

passengers who reserve but don't show up : mean = 40 , Std = 14

net cost of involuntary boarding denial = $900

Determine the probability of not dealing with over booked passengers

Given ;

Net cost of Involuntary boarding denial ( Nd ) = $900

cost excess ticket ( Ct ) = $450

first step : determine the critical ratio

Cr = Nd / Ct + Nd

= 900 / ( 900 + 450 ) = 0.67

Finally determine the Prob ( of not dealing with overbooked passengers )

= 1 - 0.67 = 0.33 = 33%