Question

9. Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine desk that follows a Poisson distribution with (a) (5 points) What is the probability that at most four anomalies in that region. 0.195 (b) (5 points) What is the expected number of material anomalies occurring in that region. Elx) = 16 (C) (5 points) What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation? 0.0992

Answer 1

Q.9) Given that, X ~ Poisson (μ = 4)

E(X) = 4 and Var(X) = 4 and SD(X) = $\sqrt { Var(X)} = \sqrt 4 = 2$

a) We want to find, P(X ≤ 4)

Using Excel we find this probability,

P(X ≤ 4) = POISSON (4, 4, 1) = 0.628837

Therefore, required probability is 0.628837

b) Expected number of material anomalies occuring in that region is 4

c) mean + sd = 4 + 2 = 6

We want to find, P(X > 6)

P(X > 6)

= 1 - P(X ≤ 6)

= 1 - POISSON (6, 4, 1)

= 0.110674

Therefore, required probability is 0.110674

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