In: Statistics and Probability
Leaks occur in a pipeline at a mean rate of 4 leaks per 1,000
meters. In a 2,500-meter section of pipe,
(a) Using the Poisson approximation to the
binomial, what is the probability of no leaks? (Round your
answer to 6 decimal places.)
Probability
(b) Using the Poisson approximation to the
binomial, what is the probability of three or more leaks?
(Round your answer to 6 decimal places.)
Probability
(c) What is the expected number of leaks?
(Round your answer to 1 decimal place.)
Expected number of leaks
Answer:
Given that:
Leaks occur in a pipeline at a mean rate of 4 leaks per 1,000 meters. In a 2,500-meter section of pipe
Number of samples (n) = 2500
Sample probability (p) = 4/1000
By using the Poisson approximation
Mean
a) Using the Poisson approximation to the binomial, what is the probability of no leaks?
That is P(X=0)
We know that the probability of Poisson distribution is !
!
b) Using the Poisson approximation to the binomial, what is the probability of three or more leaks?
That is
Where
!!!
c) What is the expected number of leaks?
The expected number of leaks would be