Question

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 124 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. Round your answers to two decimal places (e.g. 98.76). (a) What is the probability that every passenger who shows up gets a seat? (b) What is the probability that the flight departs with empty seats? (c) What are the mean and (d) standard deviation of the number of passengers who show up?

Answer 1

P ( passenger does not show up) = 0.10

P ( passenger shows up ) = 1 -0.10 = 0.90

n = 125 (total tickets sold)

(a) Probability that every passanger who shows up gets the seat = P(x <= 124)

P(x <= 124) = 1- P( x= 125)

P(x <= 124) = 1- P( x= 125)

P(x <= 124) = 0.99999809316252

P( x <= 124) = 1.00 (rounding off to two decimals)

(b) Probability that flight departs with empty seats = P(x < 124) = 1- P(x > or = 124)

P(x < 124) = 1- P(x > or = 124) = 1- P (x= 124) - P(x=125)

P(x < 124) = 1- P(x > or = 124) = 1- P (x= 124) - P(x=125) = 0.99997160930861

P(x < 124) = 0.99997160930861

P(x <124) = 1.00 (rounding off to two decimals)

(c) Mean

mean = n = 125 * 0.90= 112.5

(d) SD