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 ≤ 4) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X ≤ 4) =
(b) Determine P(X = 1) from the pmf formula. P(X = 1) = Determine P(X = 1) from the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X = 1) =
(c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) =
(d) What is the probability that X exceeds its mean value by more than one standard deviation?

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

Why is studying fractions important

Identify one charcteristic of exponential growth