Choose better bank queue and describe distributions

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, …). 1. Sketch the distribution of **number of connections per user**. 2. Give a plausible **range for the mean** (order-of-magnitude is fine) and explain what data properties drive it. 3. For this distribution, compare **mean vs. median vs. mode** (which is largest?) and explain why.