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
A Level Statistics (and IAL S1): probabilities, percentage points, finding μ or σ, and the normal as an approximation to the binomial (with a continuity correction).
Practise it: Statistical distributions · IAL S1.
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.
Normal distribution on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- MENU 7 (Distribution) → 2 (Normal CD) → 2 (Variable).
- Lower 45 =, Upper 60 =, σ 8 =, μ 50 =, then =.
- Inverse: MENU 7 → 3 (Inverse Normal) → Variable. Area 0.9 (the area to the left), σ 8, μ 50.
- For P(X > 62): Lower 62, Upper 1×10⁹⁹. For a right-tail inverse use Area = 1 − p.
Normal distribution on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
- HOME → Distribution → Normal CD → Variable.
- Lower 45, Upper 60, σ 8, μ 50, then EXE.
- Inverse: Distribution → Inverse Normal → Variable, Area 0.9, σ 8, μ 50.
- The area for Inverse Normal is the left-tail area (use 1 − p for a right tail) unless your screen offers a Tail setting.
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 allowed in A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- 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.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- 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.