Question

(a) Find the probability that the company will meet ts goal on a particular Probablaty Probability mm on a

Answer 1

a)

expected number of failure in 100 miles =6*2=12 =$\lambda$

hence P(meet its goal)=P(X<=6) =$\sum_{x=0}^{6}e^{-\lambda }\lambda ^{x}/x!$ =0.0458

b)P(not meet its goal) =1-P(meet goal) =1-0.0458 =0.9542

c)

expected number of failure in 200 miles =6*4 =24=$\lambda$

P(X<=6) =$\sum_{x=0}^{6}e^{-\lambda }\lambda ^{x}/x!$ =0.0000

d)

expected number of failure in 150 miles =6*3=18 =$\lambda$

P(X>12) =1-P(X<=12) =1-$\sum_{x=0}^{12}e^{-\lambda }\lambda ^{x}/x!$ =1-0.0917 =0.9083