# Corrected commute model

Primary model: continuous right-skewed lognormal, moment-matched to a two-regime planning description.

- Ordinary days: mean 30.0 min, SD 5.0 min.
- Accident days: mean 60.0 min, SD 15.0 min.
- Accident probability: 10%.
- Mixture-implied mean: (1-p)*30 + p*60 = 33.000000 min.
- Mixture-implied variance: (1-p)*(5^2+(30-mean)^2)+p*(15^2+(60-mean)^2) = 126.000000 min^2.
- Moment-matched SD: 11.224972 min.
- Lognormal parameters: mu=3.441765, sigma=0.330884.

Five mornings are independent. For per-morning late probability q:
P(at most one late in five)=(1-q)^5+5q(1-q)^4.
The 95% weekly requirement implies q <= 0.076440.

At a 52-minute buffer, the executed model gives daily late probability 0.061811 and weekly success probability 0.966302 (96.6%), versus the 95.0% requirement. This is 22 minutes beyond the usual 30-minute commute.

The accident-probability sensitivity curve evaluates p=2%, 5%, 10%, and 20% for both the corrected two-state mixture and the continuous moment-matched lognormal; values are in the CSV and figure.

Every number in this file, the CSVs, and the figure was generated by the executed Python code for this run.
