Question

In: Statistics and Probability

Leaks occur in a pipeline at a mean rate of 4 leaks per 1,000 meters. In...

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

Solutions

Expert Solution

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

orchestra answered 2 years ago

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