Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article “Methodology for Probabilistic Life Prediction of Multiple- Anomaly Materials” (Amer. Inst. of Aeronautics and Astronautics J., 2006: 787–793) proposes a Poisson distribution for X. Suppose that ? = 4. a. compute both P (X ? 4) and P ( X < 4). b. Compute P( 4 ? X ? 8) c. compute P (8 ? X). d. ?What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation?

Solution : Step 1 : Here X is the number of material anomalies occurring in particular region of an aircraft gas- turbine disk. And the article propose a poisson distribution X with = 4. Based on this we have to compute different probability.