Context

You are interviewing for a Data Scientist role focused on analytics and experimentation. An amusement park is considering launching a paid FastPass. You will estimate capacities, wait times, and revenue impact; then propose an experiment and guardrails.

Given

• Park hours: 10:00–20:00 (10 hours).
• Rides (batch service):
  • RollerCoaster: 24 seats/dispatch, dispatch every 3 min.
  • DropTower: 16 seats/dispatch, dispatch every 2 min.
  • Carousel: 40 seats/dispatch, dispatch every 5 min.
• Attendance: 6,000 guests/day; arrivals uniform over the day.
• Willingness to ride at least once: 60% RollerCoaster, 50% DropTower, 80% Carousel.
• For any guest who is willing, average rides on that ride = 1.2 (i.e., expected rides per guest = willingness × 1.2).
• Admission price: $60.
• Optional FastPass: $30, reserves time slots and uses 15% of each ride’s capacity.

Tasks

1. Capacity and wait times
   • 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 should not exceed 95% of capacity to avoid nonlinear queuing. State assumptions.
2. FastPass recommendation
   • Recommend whether to launch FastPass and at what price/cap.
   • Quantify expected change in revenue and average wait times, accounting for capacity reallocation to FastPass users and potential cannibalization of regular rides.
3. Experiment design (2 weeks)
   • Specify unit of randomization, sample-size drivers, primary and guardrail metrics (e.g., revenue/guest, wait time, NPS, churn/refund), and controls for day-of-week and weather.
   • Include a pre-analysis plan (MDE, CUPED or stratification) and a stopping rule.
4. Error-catching
   • You once multiplied a throughput number by mistake. Propose two independent, fast sanity checks to catch such arithmetic errors in real time (e.g., dimensional analysis and redundant aggregation cross-checks).