How to do a normal distribution (normal cdf and inverse normal) on the Casio fx-CG50
P(a < X < b) with normal cdf, and the value for a given probability with inverse normal, including finding σ or μ. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
Normal distribution questions appear on almost every AA and AI Paper 2: probabilities, the value with a given percentage below it, and (harder) finding an unknown μ or σ with the standard normal Z. Write the probability statement, e.g. P(45 < X < 60), before the answer.
Practise it: SL AA normal distribution · SL AI normal distribution · HL AA normal distribution · HL AI normal and Poisson.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Normal distribution on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- MENU 2 (STATISTICS), then F5 (DIST) F1 (NORM).
- Probability: F2 (Ncd). Data: Variable. Lower 45, Upper 60, σ 8, μ 50 (EXE after each). Move to Execute and press EXE (or F1 CALC).
- One-sided: for P(X > 62) use Lower 62, Upper 1E99 (type 1 ×10ˣ 99); for P(X < k) use Lower −1E99.
- Inverse: F3 (InvN). Tail: Left, Area 0.9, σ 8, μ 50, then Execute.
- Finding σ or μ: InvN with σ = 1, μ = 0 gives z, then solve z = (x − μ) ÷ σ.
- The Casio order is σ before μ. Entering 50 then 8 finds N(8, 50²).
- InvN's Tail can be Left, Right or Central, so P(X > k) = 0.1 can be done directly with Tail: Right.
- From RUN-MATRIX the same functions are under OPTN F5 (STAT) F3 (DIST) F1 (NORM): NormCD(45, 60, 8, 50).
Normal distribution on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- 2nd vars (DISTR) → 2: normalcdf(.
- lower: 45, upper: 60, μ: 50, σ: 8. Paste, enter.
- One-sided: use 1E99 (1 2nd , (EE) 99) or −1E99 as the missing bound.
- Inverse: 2nd vars → 3: invNorm(. area: 0.9, μ: 50, σ: 8, Tail: LEFT (the Tail option is on OS 5.x). enter.
- TI order is μ then σ (the opposite of Casio).
- normalpdf (item 1) is the height of the curve, not a probability: never use it for P(X = a) or P(a < X < b).
Normal distribution on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Calculator page: menu → Probability → Distributions → Normal Cdf.
- Lower Bound 45, Upper Bound 60, μ 50, σ 8. OK.
- Use ∞ from the π▸ key (or 1E99) for a missing bound.
- Inverse: menu → Probability → Distributions → Inverse Normal. Area 0.9, μ 50, σ 8. OK.
- Inverse Normal uses the area to the left.
Worked example
X ~ N(50, 8²). Find (a) P(45 < X < 60), (b) P(X > 62), (c) k with P(X < k) = 0.9. (d) Y ~ N(50, σ²) with P(Y < 70) = 0.95: find σ.
Answers (checked with Python)
(a) 0.628365. (b) 0.0668072. (c) k = 60.2524. (d) invNorm(0.95) = 1.64485, so σ = 20 ÷ 1.64485 = 12.1591.
Common calculator mistakes
- Casio wants σ before μ; TI and TI-Nspire want μ before σ.
- Typing the variance instead of the standard deviation: N(50, 64) means σ = 8.
- Using normalpdf / Npd for a probability.
- Inverse normal with a right-tail area: P(X > k) = 0.1 means the left area is 0.9.
- Rounding z or an intermediate probability before the last step.
Do it in Desmos
Not in the exam. Desmos is not an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- Type N = normaldist(50, 8). Desmos draws the curve.
- N.cdf(45, 60) gives P(45 < X < 60); tick the shading option in the distribution to see the area.
- N.inversecdf(0.9) gives k for P(X < k) = 0.9.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
N=normaldist(50,8)N.cdf(45,60)N.inversecdf(0.9)
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.