The monthly worldwide average number of airplane crashes of commercial

Idilwsiw2

Idilwsiw2

Answered question

2021-11-12

The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be (a) more than 2 such accidents in the next month? (b) more than 4 such accidents in the next 2 months? (c) more than 5 such accidents in the next 3 more than 5 such accidents in the next 3 months? Explain your reasoning!

Answer & Explanation

Cherry McCormick

Cherry McCormick

Beginner2021-11-13Added 23 answers

If N as the random variable that marks the number of plane crashes in a certain month. Use Poisson approximation since we are given that the average number of crashes is 2.2.
N pois 
a) P(N>2)=1P(N=0)P(N=1)P(N=2) =1e2.22.2e2.22.222!e2.20.3773 
 

b) Since the average number of crashes in one month is 2.2, the average number of crashes in two months is 4.4. Hence, if we say that N1 is the number of crashes in two months, we have that N1 pois.
P(N1>4)=1P(N1=0)P(N1=1)P(N1=2)P(N1=3)P(N1=4) =1k=044.4kk!e4.40.44882 
c) N2 marks the number of crashes in next three months, using the same argument as in a) have that N2. Hence 
P(N2>5)=1k=056.6kk!e6.60.64533

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