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).

This question evaluates capacity planning, queuing theory (Little's Law), revenue and cannibalization modeling, A/B experiment design (randomization, sample-size and pre-analysis planning), and quick arithmetic sanity checks for a Data Scientist role in Analytics & Experimentation.

How do I approach Analytics & Experimentation interview questions?

Analytics & Experimentation questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master analytics & experimentation interviews.

What difficulty level is this interview question?

This is a hard difficulty Analytics & Experimentation question, commonly asked during Technical Screen rounds at Capital One.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Capital One during technical interviews.

Optimize amusement park pricing, capacity, and testing

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

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.
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.
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.
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).

Context

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

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.
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.
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.
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).

Optimize amusement park pricing, capacity, and testing

Quick Overview

Context

Given

Tasks

Solution

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Optimize amusement park pricing, capacity, and testing

Quick Overview

Context

Given

Tasks

Solution

Comments (0)