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 μ = 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?
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