Question

Bluesky air has the best on-time arrival rate with 80% of its flights arriving on time. a test is conducted by randomly selecting 16 bluesky air flights and observing whether they arrive on time. what is the probability that 2 flights of bluesky air arrive late? (please carry answers to at least six decimal places in intermediate steps. give your final answer to the nearest four decimal places).

Answer 1

This is a binomial distribution where 80% of flights arrive on time (p = 0.8) and 20% do not (q = 1 - 0.8 = 0.2). Then the probability that exactly 2 flights arrive late follows the formula:
(nCr)(p^r)(q^(n-r)), where n = 16 (total # of flights), r = 14 (flights that arrive on time)
(16C14)(0.8^14)(0.2^2) = 0.2111