Capital One · Product & Business Case

Optimize amusement park pricing, capacity, and testing

TrueInterview

October 7, 2026 · 1 min read

A theme park is open from 10:00 to 20:00, a 10-hour day. Its three signature rides run as follows: RollerCoaster dispatches 24 seats every 3 minutes; DropTower dispatches 16 seats every 2 minutes; Carousel dispatches 40 seats every 5 minutes. Average daily attendance is 6,000 guests, arriving uniformly. The share of guests willing to ride at least once is 60% for RollerCoaster, 50% for DropTower, and 80% for Carousel; among willing guests, the average number of rides is 1.2 for each ride. Admission costs $60. You can add an optional FastPass priced at $30 that reserves a time slot and consumes 15% of each ride’s capacity.

Tasks:

Calculate the hourly and daily theoretical capacity for each ride. Apply Little’s Law ( $L = \lambda W$ ) to estimate the expected peak-hour wait time per ride, assuming uniform arrivals and assuming ride utilization must stay at or below 95% of capacity to avoid nonlinear queueing. List all assumptions.
Decide whether to launch FastPass, and recommend a price and capacity cap. Estimate the expected revenue change and the change in average wait times, including the effect of reallocating capacity to FastPass users and possible cannibalization of regular ride capacity.
Design a two-week experiment to test your recommendation. State the randomization unit, the factors that drive sample size, primary and guardrail metrics such as revenue per guest, wait time, NPS, and churn/refund rate, and how you will control for day-of-week and weather. Include a pre-analysis plan with MDE, CUPED or stratification, and a stopping rule.
During the interview, you made an arithmetic mistake while multiplying a throughput figure. Suggest two independent, quick sanity checks you would build into your workbook or notebook to catch that kind of error in real time, such as dimensional analysis and redundant aggregation cross-checks.

Overview: This case assesses capacity planning, queueing theory via Little’s Law, revenue and cannibalization modeling, A/B experiment design including randomization, sample size, and pre-analysis planning, and fast arithmetic sanity checks for a Data Scientist position in Analytics & Experimentation.

Capital One · Product & Business Case

Optimize amusement park pricing, capacity, and testing

TrueInterview

October 7, 2026 · 1 min read

Tasks:

Calculate the hourly and daily theoretical capacity for each ride. Apply Little’s Law ( $L = \lambda W$ ) to estimate the expected peak-hour wait time per ride, assuming uniform arrivals and assuming ride utilization must stay at or below 95% of capacity to avoid nonlinear queueing. List all assumptions.
Decide whether to launch FastPass, and recommend a price and capacity cap. Estimate the expected revenue change and the change in average wait times, including the effect of reallocating capacity to FastPass users and possible cannibalization of regular ride capacity.
Design a two-week experiment to test your recommendation. State the randomization unit, the factors that drive sample size, primary and guardrail metrics such as revenue per guest, wait time, NPS, and churn/refund rate, and how you will control for day-of-week and weather. Include a pre-analysis plan with MDE, CUPED or stratification, and a stopping rule.
During the interview, you made an arithmetic mistake while multiplying a throughput figure. Suggest two independent, quick sanity checks you would build into your workbook or notebook to catch that kind of error in real time, such as dimensional analysis and redundant aggregation cross-checks.