☕ The Stats Cafe

Click a card to master the distributions of your business.

Tap on any card to see the Why, When, and How.

Bernoulli 🎯
The "Single Passerby"
What is it?

A binary outcome: Success (1) or Failure (0).

Why use it?

To model individual yes/no events before they happen.

When?

When you focus on a single person walking past your door.

How?

Define $p$ (probability they enter). If $p=0.2$, there's a 20% chance they buy.

Binomial 👥
The "Morning Rush Group"
What is it?

Sum of multiple independent Bernoulli trials.

Why use it?

To predict outcomes for a fixed-size group of people.

When?

When 50 people walk by and you need to know how many might come in.

How?

Use number of trials ($n$) and probability ($p$) to find the likely "count."

Poisson 🕒
The "Hourly Traffic"
What is it?

Frequency of events over a continuous interval (time).

Why use it?

To manage staffing levels for unpredictable arrivals.

When?

When you want to know the chance of 100 people arriving between 8 AM - 9 AM.

How?

Based on your historical average ($\lambda$). If you average 40/hr, what's the chance of 60?

Normal ⚖️
The "Consistent Cup"
What is it?

The Bell Curve. Symmetric data clustered around a mean.

Why use it?

For Quality Control and predicting natural variations.

When?

When measuring the exact weight of coffee beans in every bag.

How?

Use the Mean ($\mu$) and Standard Deviation ($\sigma$) to see if a bag is "too light."

Exponential
The "Wait Time"
What is it?

The time between independent events.

Why use it?

To optimize workflow and customer experience.

When?

When the barista asks: "How long until I have to make the next latte?"

How?

Calculates the probability that the "gap" between customers is $> 5$ minutes.

Uniform 📏
The "Lunch Window"
What is it?

Every outcome in a range has the exact same probability.

Why use it?

When there is no clear peak or "popular" time in a window.

When?

A supplier says they will deliver milk "between 1 PM and 4 PM."

How?

The probability is spread flat across the entire time range.