BlueSky Air has the best on-time arrival rate with 80% of its flights arriving on time. A test is conducted by randomly selecting?

a) When Binomial Model is used
P(late arrival rate) = P(success) = p = 0.2
[because 100% - 80% = 20% or 0.2]
q = 1-p = 1-0.2 = 0.8
n = 16
According to Binomial Model
P(x) = nCx*p^x*q^(n-x)
Required probability = P(x=2) = 16C2*0.2^2*0.8^14
= 0.2111

b) When Poisson Model is used
On-time arrival rate = 80% = 0.8
Late arrival rate = 1 - 0.8 = 0.2
Mean = lambda = m = 16*0.2 = 3.2
P(x) = e^-m * m^x / x!
Required probability = P(x = 2)
= e^-3.2 * 3.2^2 / 2!
= 0.04076 * 10.24 / 2
= 0.20869