Question

The number of loss of separation incidents (LOS) in the airspace around a busy airport has averaged 8.7 per year. New radar was installed six months ago, since when there have been 8 LOS. Assume LOS occur randomly and independently. Suppose that the average annual rate of 8.7 LOS per year has not changed.

a) What is the average rate of LOS per six months?

b) Calculate the probability of 8 LOS in six months.

c) Calculate the probability of 8 or more LOS in six months.

d) It has been suggested that the new radar has led to an increase in LOS. Which of the two probabilities, (b) or (c), is the more relevant when considering this claim?

Answer 1

here average number of loss of seperation incidents in the airspace= 8.7per year

(a) here the average rate of LOS per six months= 8.7/2 = 4.35

(b) Here as the distribution is Poisson Distribution where x is the number of LOS in 6 months.

Pr(x= 8) = e^-4.35 (4.35)⁸ /8! = 0.0410

(c) here

Pr(x > = 8) = 1 - Pr(x <8) = 1 - POISSON (7 ; 4.35 ; true) = 1 - 0.9253 = 0.0747

(d) Here probability c is more relevent here as the probability c only include the probability of 8 claims not more than that. So,here as the probability is not less than 0.05, so we will reject the claim