Answer to Question #117885 in Statistics and Probability for Oyeshe

Question

An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a random variable with variance = 5.
(a) What is the probability that at most total 30 cars in 35 year will experience a catastrophe?
(b) What is the probability that average less than 3 cars in 35 year will experience a catastrophe?

Answer 1

(a) What is the probability that at most total 30 cars in 35 year will experience a catastrophe?  

at most 6 time per 7 years:

Expected per 7 years λ= 5*7=35

P(x=X)=e^-λ*λ^X/X!

P(x≤6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)=6.30511676e-16+2.20679087e-14+3.86188401e-13+4.50553135e-12+3.94233993e-11+2.75963795e-10+1.60978881e-9=1.93009042e-9

at most  30 cars in 35 year: p =P(at most 6 car per 7 years)^5=1.93009042e-9^5=2.67847918e-44

(b) What is the probability that average less than 3 cars in 35 year will experience a catastrophe?

Expected per 35 years λ= 5*35=175

P(x<3)=P(x=0)+P(x=1)+P(x=2)=9.96473301e-77+1.74382828e-74+1.52584974e-72=1.54338767e-72