Question

According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question.

A) At least 3 flights are not on time.

B) At the most 8 flights are on time.

C) In between 6 and 9 flights are on time.

Answer 1

Let X be the number of flights that are not on time among the 10 flights

Each flight getting delayed is independent of another

Therefore X follows binomial distribution with n = 10 and p = 0.15

where x = 0,1,2,...n

where x = 0,1,2....10

a)

Therefore the probability that at least 3 flights are not on time = 0.1798

b) At most 8 flights are on time ==> at least 2 flights are not on time

Therefore the probability that at the most 8 flights are on time is 0.4557

c) 6/7/8/9 flights are on time ==> 4/3/2/1 flights are not on time

Therefore the probability that between 6 and 9 flights are on time is 0.7933