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?

a)

b)

c)

d)

Step-by-step explanation:

Let X the random variable that represent the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. We know that

The probability mass function for the random variable is given by:

And f(x)=0 for other case.

For this distribution the expected value is the same parameter

 , ,

a. Compute both P(X≤4) and P(X<4).

Using the pmf we can find the individual probabilities like this:

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?

The mean is 4 and the deviation is 2, so we want this probability