Business Context

QuickCart tracks delivery times to set customer expectations and manage service-level targets. A data analyst is asked to explain when a normal model is appropriate, how skewness changes interpretation, and how to compute basic probabilities from observed outcomes.

Problem Statement

You are given summary data for two operational metrics: delivery time and order value. Delivery time is approximately symmetric and can be modeled as normal; order value is right-skewed. Use the data to compute probabilities and explain how distribution shape affects business interpretation.

Given Data

Requirements

1. Briefly define a normal distribution and explain why delivery time may fit it.
2. Compute the probability that a delivery takes more than 40 minutes.
3. Compute the probability that a delivery takes between 28 and 36 minutes.
4. Explain skewness using the order value data and state whether mean or median is the better “typical” summary.
5. Compute the overall probability that an order is late using the law of total probability.
6. State one practical implication of assuming normality for a skewed variable.

Assumptions

• Delivery times are independent across orders.
• The normal model for delivery time is acceptable for probability calculations.
• Historical conditional probabilities are stable over the analysis period.