A particular project network has two paths through it: Path A and Path B. Path A has an expected completion time of 15 weeks and a variance in completion time of 8 weeks, while Path B has an expected completion time of 16 weeks and a variance in completion time of 4 weeks. What is the probability that this project is going to take more than 18 weeks?

Probability that this project is going to take more than 18 weeks = 0.99991

Step-by-step explanation:

When independent distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

For this distribution, the total time the project will take = A + B

A ~ (15, 8)

B ~ (16, 4)

Combined mean = μ₁ + μ₂ = 15 + 16 = 31

Combined variance = 1²σ₁² + 1²σ₂² = 8 + 4 = 12

Combined Standard Deviation = √(12) = 3.464 weeks

So, with the right assumption that this combined distribution is a normal distribution

Probability that this project is going to take more than 18 weeks

P(x > 18)

We first normalize/standardize 18

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (18 - 31)/3.464 = - 3.75

The required probability

P(x > 18) = P(z > -3.75)

We'll use data from the normal probability table for these probabilities

P(x > 18) = P(z > -3.75) = 1 - P(x ≤ -3.75)

= 1 - 0.00009 = 0.99991

Hope this Helps!!!

answer: true

step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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