Question

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"t proposes a Poisson distribution for X. Suppose that μ-4. (Round your answers to three decimal places.) (a) Compute both P(X S 4) and P(X < 4). P(X < 4)- (b) Compute P(4 sX 9) (c) Compute P(9 sX) (d) What is the probability that the number of anomalies does not exceed the mean value by more than one standard deviation? You may need to use the appropriate table in the Appendix of Tables to answer this question

Answer 1

a)P(X<=4 )= $\sum_{x=0}^{4}e^{-4}4^{x}/x!$ =0.629

P(X<4) = $\sum_{x=0}^{3}e^{-4}4^{x}/x!$ =0.433

b)

P(4<=X<=9)= $\sum_{x=4}^{9}e^{-4}4^{x}/x!$ =0.558

c)P(9<=X) =1-P(X<=8) =1- $\sum_{x=0}^{8}e^{-4}4^{x}/x!$ =1-0.979 =0.021

d)P(X<=4+2)=P(X<=6)=0.889