Flying over the western states with mountainous terrain in a small aircraft is 4
ID: 3207009 • Letter: F
Question
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 2.4 accidents per 100,000 flight operations.
a) Let r= number of accidents for a given number of operations. Explain why the Poisson distribution would be a good choice for the probability distribution of r.
b) Find the probability of no accidents in 100,000 flight operations. (Use 4 decimal places.)
c) Find the probability of at least 5 accidents in 200,000 flight operations. (Use 4 decimal places.)
Explanation / Answer
Solution:
a) In a Poisson Distribution the probability of success gets smaller and smaller as the number of trials gets larger and larger. so in this distribution number of accidents are very small as compared to number of operations, the number of trials are getting larger and larger.
b) The probability of no accidents in 100,000 flight operations is P(r = 0) = 0.0907
By appplying poisons distribution:-
P(r; ) = (e-) (r) / r!
= 2.4, r = 0
P(r = 0) = 0.09071795
c) The probability of at least 5 accidents in 200,000 flight operations is P(r = 5) = 0.1747.
There are 2.4 accidents per 100,000 flight operations.
For 200,000 flight operations expected number of accidents = 2 × 2.4 = = 4.8
By appplying poisons distribution:-
P(r; ) = (e-) (r) / r!
= 4.8, r = 5
P(r = 5) = 0.174747