Question

When someone buys a ticket for an airline​ flight, there is a 0.0973 probability that the person will not show up for the flight. A certain jet can seat 17 passengers. Is it wise to book 19 passengers for a flight on the​ jet? Explain. Determine whether or not booking 19 passengers for 17 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet. ​(Round to four decimal places as​ needed.)

Answer 1

SOLUTION:

From given data,

When someone buys a ticket for an airline​ flight, there is a 0.0973 probability that the person will not show up for the flight. A certain jet can seat 17 passengers. Is it wise to book 19 passengers for a flight on the​ jet? Explain.

This will be a binomial experiment with parameters:

n = 19,

p = P(Person will show up) = 1 - 0.0973 = 0.9027

Determine whether or not booking 19 passengers for 17 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet.

P(X > 17) = P (X = 18) + P(X=19)

P(X > 17) = ¹⁹C₁₈ * 0.9027¹⁸ * (1-0.9027)^19-18 + ¹⁹C₁₉ * 0.9027¹⁹ * (1-0.9027)⁰

P(X > 17) = 19*0.1584097 * 0.0973 + 1 * 0.1429964 * 1

P(X > 17) = 0.29285201239+ 0.1429964

P(X > 17) = 0.4358

(or)

P(X > 17) = 1 - P(X < 16)

P(X > 17) = 1 - binomdist(16, 19, 0.9027, TRUE) [Excel Formula]

P(X > 17) = 0.4358