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"� proposes a Poisson distribution for X. Suppose that ? = 4. (Round your answers to three decimal places.) (a) Compute both P(X ? 4) and P(X < 4). (b) Compute P(4 ? X ? 5). (c) Compute P(5 ? X). (d) What is the probability that the number of anomalies does not exceed the mean value by more than one standard deviation?

Answer 1

0.6284,0.4335,0.1953.0.9786

Explanation:

Given that X the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk is following a poisson distribution with parameter 4

a)
`P(X\leq 4)=0.6284\\P(X<4)=0.4335`

b)
`P(4\leq x<5)\\=P(4)=0.1953\\`

c) P(
`5\leq x)`=0.8046

d) the probability that the number of anomalies does not exceed the mean value by more than one standard deviation

=
`P(0\leq X\leq 8)\\=F(8)-F(0)\\=0.9786`