An HR department uses an AI screening tool to detect a highly specialized engineering skill. Only 2% of candidates actually possess this skill (P(Skill) = 0.02). If a candidate has the skill, the AI correctly flags them 95% of the time. However, the AI also falsely flags 10% of candidates who do not

have the skill.

If a candidate is flagged by the AI as HAVING the skill (

An automated robotic painting arm (1 server) operates with a constant processing time of exactly 24 seconds per vehicle. Vehicles arrive randomly on the conveyor belt following a Poisson distribution at a rate of 120 vehicles per hour. What is the expected average number of vehicles waiting in the queue E(L) before being painted?

An industrial washing station features a single bay (1 server). Vehicles arrive randomly following a Poisson distribution at a rate of 1 vehicle every 4 minutes. The washing bay takes exactly 5 minutes to process a vehicle (exponentially distributed).

A floor supervisor argues that because the wash takes only 5 minutes, the queue will naturally stabilize. According to queueing theory, what is the exact state of this system, and what is the minimum number of parallel servers (

An industrial company has Total Assets amounting to €2,500,000 and Long-term Debts of €1,500,000. It has no short-term debts. Last year, the company generated a Gross Margin (before interest) of €200,000. The interest rate on their debt is a flat 4%.

Assuming Assets = Equity + Debt, what is the company's Return on Equity (

A firm is considering investing €500,000 in a new tire assembly line. The project will generate a raw, unadjusted cash flow of €235,000 annually. The company's standard interest rate without inflation is 5%. However, the finance department expects a steady inflation rate of 1% and wants to evaluate the project using "euros taking inflation into account" (actual quantities) rather than modifying the cash flows directly.

To correctly assess this project using the dynamic NPV method, what must the financial analyst do to the interest rate, and what is the exact rate they should apply?

In an assembly line, 4% of microchips are inherently defective (P(D) = 0.04

). An automated optical inspector is designed to reject defective chips. It successfully rejects a defective chip 95% of the time. However, it also falsely rejects 2% of perfectly good chips.

A chip passes through the inspector and is

You are designing a PERT graph for a Polaris missile subsystem. Activity B and Activity C can be executed simultaneously, but both can only start after Activity A is fully completed. Furthermore, Activity D cannot begin until both

Activity B and Activity C are finished.

If you draw this network exactly as described, what structural element is strictly mandatory to include between the events marking the completion of B and C, and why?

A manager tracks a critical spare part. The daily demand is highly variable. During the constant 4-day delivery period, the average demand is 200 units (mu = 200) with a standard deviation of 30 units (sigma = 30

).

The manager has configured the ERP system to trigger a new order exactly when the total stock drops to 248 units. Based on the standard normal distribution table used in class, what exact Service Level is the manager targeting?

A telecom company models customer accounts using a Markov transition matrix. The states are: "Active" (Transient), "Suspended" (Transient), "Closed" (Absorbing), and "Sent to Collections" (Absorbing).

To predict how many currently "Suspended" accounts will eventually end up "Sent to Collections", the analyst calculates the Fundamental Matrix

A factory purchases raw materials. The standard unit price is c1. The supplier offers a discounted price c2 (c2 < c1) if the factory orders a quantity greater than a threshold h. The supply chain manager calculates the standard Economic Order Quantity (Q) using price c1 and finds that Q < h

.

To minimize total costs, the manager must evaluate a specific point "a". What does point "a" mathematically represent in the context of the cost functions