Topic Brief: Normal Distribution Standardisation and Conditional Probability

#SIGNAL Topic Master Brief — The Normal Distribution: Standardisation and Conditional Probability (WST01, spec 6.1/3.2)

Provenance (2026-09-29): built entirely from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25), re-read in full for §5 Section 6, the 2026-09-12 per-lesson audit of normal-distribution-standardisation-and-conditional-probability.ts, and the assessment-structure table in §2. Cross-checked against signal-frequency-and-boundaries.md and codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md (both in this folder) so this document does not restate either — those two already give the "5 of 6" frequency row, the Jan 2023 17-mark figure, the four-way conditional-probability taxonomy, and a full series-by-series "angle tested" table. This document adds the layer neither covers as its own subject: how the marks inside a Normal-distribution question are actually structured, where that question tends to sit in the paper, and a plain-language "what to expect" summary. No new PDF fetches were made; every claim below cites a series, question, and source document. content/veridian/question-bank/wst01.ts was checked and has no item on this topic yet, so there is nothing there to cross-reference.

#1. Frequency — seen in 5 of 6 series checked

The facts bank has a fully-read Principal Examiner Feedback report for 6 of the 14 WST01 series with a verified mark scheme: Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. The Normal distribution — standardisation combined with conditional probability — is confirmed tested, with at least one full question devoted to it, in 5 of those 6: Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. It is the richest single sub-topic anywhere in the facts bank (facts bank §7). The sixth, Jun 2019, was read for two unrelated gaps (box plots; a discrete random variable) and was not re-examined for this topic — its status here is genuinely unconfirmed, not assumed absent. The other 8 series (mark schemes verified, no examiner report located) were not searched for this topic.

#2. What was actually tested, by series

• Jan 2021 Q3(a)–(c), 10 marks (audited). Package weights, $W\sim N(18,5.4^2)$: (a) forward lookup, subtract-from-1 [3]; (b) inverse lookup for an unknown boundary [3]; (c) conditional probability from two overlapping thresholds [4]. Part (d), a separate combinatorics sub-question, is excluded — different spec point.
• Oct 2021 Q6(a)–(c). Book heights on shelves, $H\sim N(25.1,5.5^2)$: (a) "show that" a forward probability, 3 marks (audited); (b) inverse lookup, with both a precision failure and a sign error recorded; (c) a percentile-ratio conditional-probability misreading, described as candidates not realising a ratio applied only to the middle band of the data.
• Jun 2022 Q6(c). Conditional probability with a double inequality, mishandled as a plain subtraction the wrong way round, or as a one-sided tail alone. Pearson's own report calls this "the final part of the paper... also the most discriminating part."
• Jan 2023 Q5(a)–(e), 17 marks total — the single largest question on that paper (signal-frequency-and-boundaries.md §1). (a): the same subtract-from-1 failure as Jan 2021; (e): a conditional probability abandoned after finding one component probability, without dividing.
• Jun 2024 Q5(a)–(c). (a): the reverse subtract-from-1 failure — over-subtracting when the target was already the "less than" side; (b): the same z-value-precision failure a third time; (c): a multi-step inverse-Normal problem the report calls the hardest confirmed skill type in the archive, candidates commonly abandoning it partway through. No conditional-probability sub-part is cited for this series in the facts bank.

#3. Mark-tariff pattern

Two real, specific patterns emerge from the audited mark schemes, beyond the totals above:

• The same 3-mark standardise-and-subtract step is built differently depending on whether the sub-part says "find" or "show that." Jan 2021 Q3(a) (a plain "find") is scored M1, A1, A1, and a correct bare answer with no working shown scores full marks ("Ans only 3/3," per the audit of that lesson). Oct 2021 Q6(a) (a "show that") is scored M1, M1, A1cso for the identical underlying calculation, with no bare-answer credit at all — the final mark requires "evidence of both M's seen," reaching back across both method steps rather than just the line immediately above it. Same skill, same tariff, structurally different mark scheme, purely because of the command word.
• Position in the paper is not fixed, but the conditional-probability sub-part is consistently the last lettered part of its question wherever its position is citable. Jan 2021 Q3(c) is the last of (a)–(c) audited (part (d) is a different spec point); Oct 2021 Q6(c) is the last part of Q6; Jun 2022 Q6(c) is explicitly "the final part of the paper" in Pearson's own words; Jan 2023 Q5(e) is the last of five lettered parts. The question itself also sits late in its paper twice over: Oct 2021 and Jun 2022 both put this content at Q6 of a confirmed 6-question paper — literally the last question (facts bank §2) — while Jan 2021 places it at Q3 of 6 and Jun 2024 at Q5 of 6, second-to-last. It is not safe to tell a student "this is always the last question," but it is fair to say the conditional-probability step, when present, does not arrive early inside its own question.

#4. If this topic appears, here's what to expect

Expect a multi-part question that opens with an ordinary forward or inverse standardisation and, in most of the confirmed series, closes with a conditional probability built from two Normal thresholds — the part every examiner report that discusses it flags as the hardest or most discriminating in the question. A "find" sub-part can be safely answered with a bare, sufficiently precise final value; a "show that" sub-part cannot — both method steps have to be visible, not just the answer. Whichever direction the standardisation runs, check by diagram whether the answer needs subtracting from 1, since the confirmed errors run in both directions across different series, not just one. Any z-value taken from the Percentage Points table needs its full 4 decimal places, and its sign has to be reasoned from the diagram rather than copied from a nearby working line. If a probability is conditional, dividing by the conditioning event's own probability is a separate, easily-skipped last step — two series record students stopping just before it.

#Sources and limitations

• All citations trace to research/veridian/WST01-verified-facts.md §2 (question-count table), §5 Section 6 (the trap catalogue), §7 (topic-richness ranking), and the 2026-09-12 per-lesson audit of normal-distribution-standardisation-and-conditional-probability.ts (Jan 2021 Q3 and Oct 2021 Q6(a) mark-scheme detail).
• Frequency is stated only as "N of 6 series checked" — no percentage or likelihood claim is made, and no grade-boundary figure is used (none exists in the source material; see signal-frequency-and-boundaries.md §2).
• Individual sub-part mark values beyond those quoted above (Oct 2021 Q6(b)/(c), Jun 2022 Q6(c), Jan 2023 Q5(b)–(d), Jun 2024 Q5(a)–(c)) are not stated as numbers anywhere in the facts bank as currently compiled — this document reports only the tariffs that are actually written down, not an estimate.
• The 8 series without a located examiner report (Jun 2021, Jan 2022, Oct 2022, Jun 2023, Oct 2023, Jan 2024, Oct 2024, Jan 2025) are excluded from both the numerator and denominator throughout.
• This document does not repeat the formal derivations, the four-way conditional-probability structural taxonomy, or the full series-by-series "angle tested" synthesis table already in codex-deep-dive-normal-distribution-standardisation-and-conditional-probability.md, nor the whole-paper frequency and mark-weight row already in signal-frequency-and-boundaries.md.