Normal Distribution (CAIE S1): Z-Tables, Reverse Lookups & Binomial→Normal

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Normal Distribution (CAIE S1): Z-Tables, Reverse Lookups & Binomial→Normal

SAT Score Range

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3 sessions

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About

We’ll master the Normal Distribution exactly as used in CAIE S1. In Session 1 we’ll set up the notation X ~ N(μ, σ²), review when a Normal model is appropriate, and learn to standardize with Z = (X − μ)/σ. We’ll read Z-tables accurately and handle every forward-probability variation (left/right tails, between/outside intervals, complements, symmetry, and careful decimal lookups). In Session 2 we’ll flip the process (“reverse” problems): find z or x from a given probability/percentile, decide the correct side(s) of the curve, and solve past-paper style questions including unknown μ or σ. In Session 3 we’ll connect Binomial and Normal: check conditions (e.g., np and n(1−p) sufficiently large), map B(n, p) → N(μ = np, σ = √(np(1−p))), apply continuity correction, and tackle mixed exam questions. 
Expect short mini-lectures, live worked examples from past papers, and time to try problems before we compare solutions.
Prereqs: comfort with basic probability and the binomial distribution (parameters n, p), plus very light algebra. Bring a calculator and a Z-table (optional).

Tutored by

Tasheen U 🇧🇩

Certified in 16 topics

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A recent graduate of CAIE A-levels with Mathematics, Physics, and Computer Science. Currently, pursuing my B.Sc. in Computer Science & Engineering. Passionate about math and education, I am eager to help others excel in subjects including math, physics, computer science, and SAT Prep. Excited to tutor in various math areas such as Algebra, Geometry, Pre-Calculus, Calculus, and Statistics. Let's learn and grow together!

Sessions

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✋ ATTENDANCE POLICY

This is a compact 3-part mini-series designed to build step-by-step. Please join on time and plan to stay for the full session.

You’ll be asked to attempt problems during class; quiet environment and chat/voice participation are appreciated.

If you miss Session 1, Session 2 may be difficult to follow; if you miss Session 2, Session 3 (binomial→normal) will be hard.

Thanks for committing to the full sequence and staying engaged throughout.

SESSION 1

14

Nov

SESSION 1

Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution

Fri 4:30 AM - 6:00 AM UTCNov 14, 4:30 AM - 6:00 AM UTC

Goal: build foundations and handle all forward Normal-probability variations.
• Notation & conditions: X ~ N(μ, σ²), standardizing with Z = (X − μ)/σ; what Z-tables report. 
• Sketch–shade–standardise method and decide the correct region on the x-axis.
• Seven forward patterns: P(X < a), P(X > a), P(a < X < b), P(X < a or X > b), complements, symmetry, and extreme-tail reading with careful row/column decimals.
• Quick checks to avoid common sign/table mistakes.
Practice: several past-paper style examples; you try first, then we compare full solutions.

SESSION 2

17

Nov

SESSION 2

Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution

Mon 3:30 AM - 4:45 AM UTCNov 17, 3:30 AM - 4:45 AM UTC

Goal: solve “backwards” Normal questions and parameter-finding tasks.
• Reading a probability and locating the region (left/right/middle) before using the table.
• Finding critical values: given p, get z, then x = μ + zσ.
• Percentiles/quantiles language (e.g., 90th percentile), and interpreting “middle c%”.
• Mixed problems: unknown μ or σ from a percentile; comparing two cut-scores.
• Targeted exam practice with fully worked solutions and common pitfalls to avoid.

SESSION 3

20

Nov

SESSION 3

Random variables and probability distributions

Thu 3:30 AM - 4:45 AM UTCNov 20, 3:30 AM - 4:45 AM UTC

Goal: connect Binomial and Normal models for approximation questions.
• When an approximation is appropriate (typical size checks on np and n(1−p)).
• Map B(n, p) → N(μ = np, σ = √(np(1−p))) and standardize.
• Continuity correction done right: translate statements like X ≥ k, X ≤ k, a ≤ X ≤ b.
• Forward and reverse styles; mixed exam questions linking binomial and normal.
• Tips for notation, rounding, and explaining your choice of approximation.

Public Discussion

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Nov 14 - Nov 20

1 week

75 - 90 mins

/ session

Next session on November 14, 2025

SCHEDULE

Friday, Nov 14

4:30AM

Monday, Nov 17

3:30AM

Thursday, Nov 20

3:30AM