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Choose better bank queue and describe distributions

LinkedInData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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This question tests your ability to apply basic queueing theory to compare waiting times and your ability to reason about how distributional shape affects central tendency measures.

Part 1: Queueing Optimization

You are standing in a bank lobby with two lines. Line A is served by one teller, and Line B is served by two tellers. Each teller processes customers at an average rate of 10 minutes per customer (exponentially distributed). You observe that Line A has 3 people currently in line, while Line B has 6 people waiting. Which line should you join to minimize your expected wait time? Explain your reasoning.

Part 2: Distributional Reasoning

A retail store tracks the time customers spend in the store. You are given a dataset of durations that follows a bimodal distribution, whereas the checkout processing times follow a right-skewed unimodal distribution.

  1. For the store duration (bimodal), how do the mean, median, and mode typically relate to one another? Is the mean a representative metric for a 'typical' customer?
  2. For the checkout time (right-skewed), if the store manager wants to improve the experience for the 'average' customer, which metric (mean or median) would be more robust to a small number of customers who have massive, outlier-sized baskets?

Hints

Hint 1

For Part 1, consider that the rate of a system with 'n' servers is the sum of the individual server rates, and wait time is proportional to the number of people divided by the total service rate.

Hint 2

For Part 2, recall that in a bimodal distribution, the mean is often pulled toward the center of the two peaks, potentially landing in a region where few customers actually exist.

Hint 3

For the skewed distribution, consider how the mean is sensitive to extreme values in the tail compared to the median, which relies on the rank-ordering of data.

Follow-up questions

  • How would your decision in Part 1 change if the service times were constant (deterministic) rather than exponentially distributed?
  • If the bimodal distribution in Part 2 represents two distinct customer segments (e.g., 'browsers' vs. 'urgent shoppers'), how would you handle these segments differently in your analysis?
  • What statistical tests would you use to determine if the difference between the two queues' wait times is statistically significant?