The science
The Laplace mechanism releases M(D) = f(D) + Lap(b), where the noise density is p(x) = exp(-|x|/b) / (2b).
sensitivity delta = max over neighbours D, D' of |f(D) - f(D')|
noise scale b = delta / epsilon
mean |error| = b variance = 2 b^2
p(M(D)=y) / p(M(D')=y) <= exp(epsilon) (epsilon-differential privacy)
Queries here: a count (changing one person changes it by at most 1), a sum of commute minutes clipped to [0, 120] (delta = 120) and a mean (delta = 120/n). Clipping is what makes the sensitivity finite; it also introduces a small bias that this lab does not display.
The dashed pink curve is the density for a neighbouring dataset whose true answer differs by delta; the ratio of the two curves never exceeds e^epsilon, which is the privacy guarantee. Smaller epsilon means stronger privacy and larger noise: the trade-off graph is the line b = delta/epsilon on log axes.
Independent check: samples are drawn by inverse-CDF, and the empirical variance is compared with 2b^2. The allowed band is 4 standard errors, using var(sample variance) ~ (kurtosis-1)/N = 5/N for a Laplace law. Simplifications: one single release per query (no composition across repeated queries; releasing many samples here is for illustration only, an attacker with many independent releases would average the noise away), floating-point sampling instead of the discrete mechanism, and a synthetic log-normal dataset, not real data.