Choose better bank queue and describe distributions
Quick Overview
This question evaluates probabilistic reasoning and statistical intuition—queueing theory for expected waiting time and variability plus distributional reasoning for unimodal versus bimodal shapes and comparisons among mean, median, and mode—in the Statistics & Math domain for a data scientist role.
You are interviewing for a data role and are asked several probability/distribution questions.
1) Bank queue choice (queueing intuition)
A bank has 5 tellers.
- Option A: 1 single line feeding the next available teller (1 queue → 5 servers).
- Option B: 5 separate lines, one per teller (5 queues → 5 servers).
Question: Which option would you choose to minimize your waiting time? Explain in terms of expected waiting time and variability, and state any assumptions you need (arrival process, service-time distribution, customer behavior like line switching).
2) Sketch common real-world distributions
(a) Heights
Sketch the distribution of:
- Adult men’s heights in the US
- Adult women’s heights in the US
- The combined distribution when you mix men and women
Describe the likely shape (e.g., unimodal/bimodal), approximate symmetry/skew, and what assumptions justify that.
(b) LinkedIn connections
Let each user have a number of connections (e.g., 100, 200, 500, …).
- Sketch the distribution of number of connections per user .
- Give a plausible range for the mean (order-of-magnitude is fine) and explain what data properties drive it.
- For this distribution, compare mean vs. median vs. mode (which is largest?) and explain why.