Question

Assume that the monthly worldwide average number of airplaine crashes of commercial airlines is 2.22.2. What is the probability that there will be
(a) at most 44 such accidents in the next month?  
(b) more than 22 such accidents in the next 22 months?  
(c) exactly 88 such accidents in the next 44 months?

Answer 1

a)

Here, λ = 2.2 and x = 4
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X <= 4).
P(X <= 4) = (2.2^0 * e^-2.2/0!) + (2.2^1 * e^-2.2/1!) + (2.2^2 * e^-2.2/2!) + (2.2^3 * e^-2.2/3!) + (2.2^4 * e^-2.2/4!)
P(X <= 4) = 0.1108 + 0.2438 + 0.2681 + 0.1966 + 0.1082
P(X <= 4) = 0.9275

b)

Here, λ = 4.4 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 2) = 1 - P(X <= 2).
P(X > 2) = 1 - (4.4^0 * e^-4.4/0!) + (4.4^1 * e^-4.4/1!) + (4.4^2 * e^-4.4/2!)
P(X > 2) = 1 - (0.0123 + 0.054 + 0.1188)
P(X > 2) = 1 - 0.1851 = 0.8149

c)

Here, λ = 8.8 and x = 8
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 8)
P(X = 8) = 8.8^8 * e^-8.8/8!
P(X = 8) = 0.1344
Ans: 0.1344