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 μ = 4. (Round your answers to three decimal places.) Compute both P(X > 4) and P(X < 4).

P(X > 4) = 0.37116 = 0.371 to 3 d.p

P(X < 4) = 0.43347 = 0.433 to 3 d.p

Step-by-step explanation:

Poisson distribution formula is given as

P(X = x) = (e^-μ)(μˣ)/x!

P(X < x) = Σ (e^-μ)(μˣ)/x! (Summation From 0 to (x-1))

P(X > x) = Σ (e^-μ)(μˣ)/x! (Summation From (x+1) to the end of the distribution)

where μ = mean = 4

x = variable whose probability is required = 4

P(X > 4) represents a fraction of all possible outcomes more than the mean

P(X > 4) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=N)

P(X > 4) = 1 - P(X ≤ 4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]

Recall,

P(X=x) = (e^-μ)(μˣ)/x!

Computing this for each of them

P(X > 4) = 0.37116

P(X < 4) represents a fraction of all possible outcomes less than the mean

P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

Recall, P(X=x) = (e^-μ)(μˣ)/x!

Computing this for each of them,

P(X < 4) = 0.43347

b.an increase in a causes b to decrease

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.