An amusement park operates 10:00–20:00 (10 hours). Three flagship rides have the following operations: RollerCoaster: 24 seats/dispatch, dispatch every 3 minutes; DropTower: 16 seats/dispatch, every 2 minutes; Carousel: 40 seats/dispatch, every 5 minutes. Daily attendance averages 6,000 guests with uniform arrival. Willingness to ride at least once: 60% RollerCoaster, 50% DropTower, 80% Carousel; average rides per willing guest is 1.2 for each ride. Admission is $60. You may introduce an optional FastPass at $30 that reserves a time slot and uses 15% of each ride’s capacity. Tasks: 1) Compute hourly and daily theoretical capacity per ride. Using Little’s Law (L = λW), approximate peak-hour expected wait time per ride assuming uniform arrivals and that ride utilization cannot exceed 95% of capacity without inducing nonlinear queuing. State all assumptions. 2) Recommend whether to launch FastPass and at what price/cap. Quantify the expected change in revenue and average wait times, accounting for capacity reallocation to FastPass users and potential cannibalization of regular rides. 3) Design a 2-week experiment to validate your recommendation. Specify the unit of randomization, sample-size drivers, primary/guardrail metrics (e.g., revenue per guest, wait time, NPS, churn/refund rate), and how you’ll control for day-of-week and weather. Include a pre-analysis plan (MDE, CUPED or stratification) and a stopping rule. 4) During the interview you erroneously multiplied a throughput number. Propose two independent, fast sanity checks you would build into your workbook/notebook to catch such arithmetic errors in real time (e.g., dimensional analysis and redundant aggregation cross-checks).