diff --git a/src/charts/ArrestsOverTime.jsx b/src/charts/ArrestsOverTime.jsx
index 3c9b90b..95cb522 100644
--- a/src/charts/ArrestsOverTime.jsx
+++ b/src/charts/ArrestsOverTime.jsx
@@ -129,7 +129,9 @@ export default function ArrestsOverTime({ data, modelId }) {
 
       <ChartLegend items={[
         { shape: 'diamond', color: OBSERVED_MARK_COLOR, label: 'Observed' },
-        { shape: 'dot', color: MODELED_AGGREGATE_COLOR, label: 'Modeled (median + 90% interval)' },
+        // 95%, not 90%: these bars are the API's count_lower/count_upper, and
+        // validate_interval() defaults to 95 (the app never passes interval=).
+        { shape: 'dot', color: MODELED_AGGREGATE_COLOR, label: 'Modeled (median + 95% interval)' },
       ]} />
 
       <p style={{ fontSize: '0.75rem', color: 'var(--cv-ink-3)', marginTop: 'var(--space-1)' }}>
diff --git a/src/utils/distributionApprox.js b/src/utils/distributionApprox.js
index fb50f5f..19e9901 100644
--- a/src/utils/distributionApprox.js
+++ b/src/utils/distributionApprox.js
@@ -42,9 +42,18 @@ function standardNormalCdf(z) {
   return 0.5 * (1 + erf(z / Math.SQRT2))
 }
 
-// Peter Acklam's rational approximation of the inverse standard normal CDF
-// (probit), relative error < 1.15e-9. Supports arbitrary intervalMass.
-function probit(p) {
+/**
+ * Peter Acklam's rational approximation of the inverse standard normal CDF
+ * (probit / R's `qnorm`), relative error < 1.15e-9. Supports arbitrary
+ * intervalMass.
+ *
+ * Exported so `agrestiCoull.js` can reuse it — the app should carry exactly one
+ * probit implementation.
+ *
+ * @param {number} p - probability in (0, 1)
+ * @returns {number}
+ */
+export function probit(p) {
   const a = [-3.969683028665376e+01, 2.209460984245205e+02, -2.759285104469687e+02, 1.383577518672690e+02, -3.066479806614716e+01, 2.506628277459239e+00]
   const b = [-5.447609879822406e+01, 1.615858368580409e+02, -1.556989798598866e+02, 6.680131188771972e+01, -1.328068155288572e+01]
   const c = [-7.784894002430293e-03, -3.223964580411365e-01, -2.400758277161838e+00, -2.549732539343734e+00, 4.374664141464968e+00, 2.938163982698783e+00]
@@ -70,11 +79,15 @@ function probit(p) {
 
 /**
  * @param {{median:number, lower:number, upper:number, intervalMass?:number, floorAtZero?:boolean}} p
- *   intervalMass: fraction of probability covered by [lower, upper] — the
- *   API's rate/count interval bounds are a 90% interval, so default 0.90.
+ *   intervalMass: fraction of probability covered by [lower, upper]. The API's
+ *   rate/count bounds are a **95%** interval — `validate_interval()` in
+ *   crdc-arrests/api/R/validate.R defaults to 95 and the app never passes
+ *   `interval=` — so the default is 0.95. Fitting 95% bounds as if they were
+ *   90% understates sigma by ~16% and draws a distribution narrower than the
+ *   model's own.
  * @returns {{ median:number, sigmaLeft:number, sigmaRight:number, pdf:(x:number)=>number, cdf:(x:number)=>number }}
  */
-export function fitSkewedInterval({ median, lower, upper, intervalMass = 0.90, floorAtZero = true }) {
+export function fitSkewedInterval({ median, lower, upper, intervalMass = 0.95, floorAtZero = true }) {
   const z = probit((1 + intervalMass) / 2)
 
   let sigmaLeft = (median - lower) / z