At an airport, 78% of recent flights have arrived on time. A sample of 14 flights is studied. Find the probability that more than 12 of them were on time.
A) 0.3761
B) 0.6239
C) 0.1527
D) 0.8473

Question

Quizplus · Accepted Answer

The probability of more than 12 flights arriving on time out of 14 can be found by calculating the probability of exactly 13 and exactly 14 flights arriving on time and adding those probabilities together. This is a binomial probability problem where n = 14, p = 0.78 (probability of success), and q = 0.22 (probability of failure). The formula for binomial probability is P(X = k) = (nCk)(p^k)(q^(n-k)), where nCk is the combination of n items taken k at a time. Calculate P(13) and P(14) and add them together to find the total probability.

At an Airport, 78% of Recent Flights Have Arrived on Time