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 2.1 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. Frequency of accidents is a rare occurrence. It is reasonable to assume the events are independent. Frequency of accidents is a rare occurrence. It is reasonable to assume the events are dependent.  Frequency of accidents is a common occurrence. It is reasonable to assume the events are independent. Frequency of accidents is a common occurrence. It is reasonable to assume the events are dependent. (b) Find the probability of no accidents in 100,000 flight operations. (Use 4 decimal places.) (c) Find the probability of at least 6 accidents in 200,000 flight operations. (Use 4 decimal places.)

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 2.1 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.
Frequency of accidents is a rare occurrence. It is reasonable to assume the events are independent.
Frequency of accidents is a rare occurrence. It is reasonable to assume the events are dependent. 
Frequency of accidents is a common occurrence. It is reasonable to assume the events are independent.
Frequency of accidents is a common occurrence. It is reasonable to assume the events are dependent.


(b) Find the probability of no accidents in 100,000 flight operations. (Use 4 decimal places.)
 

(c) Find the probability of at least 6 accidents in 200,000 flight operations. (Use 4 decimal places.)

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