Binomial y Poisson

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.)

(a) Obtain P(X =2)

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.)

Determine P(2 ≤ X ≤ 4).

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.) What is the probability that X exceeds its mean value by more than one standard deviation?

• 0.999

• 0.184

• 0.260

• 0.080

Compute the following binomial probabilities directly from the formula for b(x; n, p). (Round your answers to three decimal places.) b(5; 8, 0.3)

Compute the following binomial probabilities directly from the formula for b(x; n, p). (Round your answers to three decimal places.) b(6; 8, 0.55)

Compute the following binomial probabilities directly from the formula for b(x; n, p). (Round your answers to three decimal places.) P(3 ≤ X ≤ 5) when n = 7 and p = 0.55

Compute the following binomial probabilities directly from the formula for b(x; n, p). (Round your answers to three decimal places.) P(1 ≤ X) when n = 9 and p = 0.15

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 6 of the calls involve a fax message?

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) (c) What is the probability that at least 6 of the calls involve a fax message?

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) (d) What is the probability that more than 6 of the calls involve a fax message?