Question

Airlines A and B each operate one flight per day between the cities of Hartford and Chicago; the daily passenger volume between the two cities is 350. Because the quality of service and departure times for both airlines are similar, we assume that passengersselect the flights with equal probability and independently of one another.

Required:
a. Let X denote the number of passengers on the flight operated by airline A. Describe the exact distribution of X; name it and identify the parameters.
b. If the plane for airline A carries 210 seats there is a positive probability that more than 210 passengers will turn up, in which case not all passengers can be accommodated. Estimate the probability of "overbooking"
c. Denote by n the minimum number of seats the aircraft should contain if it is desired that the probability of exceeding the seating capacity be less than 0.01. Find n

Answer 1

X ~ (350, 0.5)

0.00009

Explanation:

Given that:

Daily passenger volume = 350

Since both airlines A and B have equal probability ;

p = 0.5

n = 350

X ~ (n, p)

X ~ (350, 0.5)

B.)

Mean, m= np = 350 * 0.5 = 175

Standard deviation, s = sqrt(np(1-p)) = sqrt(350*0.5*0.5) = sqrt(87.5)

Obtaining standardized score, Z

Z = (x - m) / s

x = 210

Z = (210 - 175) / sqrt(87.5)

Z = 35 / sqrt(87.5)

Z = 3.74

P(Z > 3.74) = 0.00009 (Z probability calculator)