Question

12#5

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 1919 Southwest flights and observing whether they arrive on time.

(a)  Find the probability that at least 55 flights arrive late  .

Answer 1

solution:-

given that n = 19

A success in this case is a flight being late so 80% of its flights arriving on time, so 100% - 80% = 20% arrive late

then p = 0.20

(a) P(x ≥ 5)

=> 1 - (P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4))

=> 1 - (19c0 * 0.20^0 * (1-0.20)^(19-0) + 19c1 * 0.20^1 * (1-0.20)^(19-1) + 19c2 * 0.20^2 * (1-0.20)^(19-2) + 19c3 * 0.20^3 * (1-0.20)^(19-3) + 19c4 * 0.20^4 * (1-0.20)^(19-4))

=> 1 - (0.0144 + 0.0685 + 0.1540 + 0.2182 + 0.2182)

=> 1 - 0.6733

=> 0.3267