Lets consider n segments of tube connected in series, whose lengths (in meters) are modeled as discrete
random variables X1, X2... Xn , independent and same distribution as P(X=k) = pq^(k-1), with k from (1,2,3.. )=N and q=1-p . For the problem in hand lets fix p=1/2. L is the total length of the tube.
a) If n=400 , determine the probability that the total length of the tube is bigger then 820 meters.
b) If n=400, determine the value of the length that is exceeded with probability 0.841.
c) Determine the value of n such that the probability of length L is at least equal to 0.841.
(HINT: Apply the central limit theorem)
