Solve the problem.
-An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at
Least 95%?
A) 167
B) 164
C) 166
D) 165

Question

Quizplus · Accepted Answer

We need to calculate the maximum number of reservations such that the probability of accommodating all reservation holders is at least 95%. Let's use the binomial distribution to solve the problem.
Let X be the number of reservation holders who show up. Then X follows a binomial distribution with parameters n = number of reservations and p = probability of showing up = 1 - 0.06 = 0.94.
We want to find the maximum value of n such that P(X ≤ 160) ≥ 0.95.
Using a binomial distribution calculator, we can find that P(X ≤ 160) = 0.9958 when n = 165. Therefore, the maximum number of reservations that the airline could accept for a flight with a capacity of 160 is 165.
Hence, the best choice is D.

Solve the Problem. -An Airline Experiences a No-Show Rate of 6%. What Is