How to do a normal distribution (normal cdf and inverse normal) on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II
On the fx-CG50: MENU → 2 (STATISTICS) → F5 (DIST) → F1 (NORM) → F2 (Ncd); inverse normal: F3 (InvN).On the TI-84 Plus CE: 2nd vars (DISTR) → 2: normalcdf(; inverse normal: 2nd vars → 3: invNorm(.On the TI-Nspire CX II: menu → Probability → Distributions → Normal Cdf; inverse normal: menu → Probability → Distributions → Inverse Normal.
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.
Which IB course and paper
| Course | GDC papers | What you use it for |
|---|---|---|
| AA SL | Paper 2 (Paper 1 is calculator-free) | Normal probabilities and inverse normal. |
| AA HL | Papers 2 and 3 (Paper 1 is calculator-free) | Also standardising (z-scores) to find an unknown μ or σ. |
| AI SL | Papers 1 and 2 | Normal probabilities and inverse normal. |
| AI HL | Papers 1, 2 and 3 | As SL, plus linear combinations of normal variables. |
A GDC is allowed on every AI paper and on AA Papers 2 and 3; AA Paper 1 is calculator-free, so learn the method by hand as well.
Topic notes: Normal distribution (AI SL) · Normal distribution and z-scores (AA SL) · Normal distribution and standardisation (AA HL) · Normal and Poisson distributions (AI HL).
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).
Watch the key presses on the fx-CG50Normal cdf · Inverse normal
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- 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.
Watch the key presses on the TI-84 Plus CENormal cdf · Inverse normal
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- 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 a different model: check the exam rules before using one).
- Calculator page: menu → Probability → Distributions → Normal Cdf.
- Lower Bound 45, Upper Bound 60, μ 50, σ 8. OK.
- For a missing bound type a very large number such as 1E99 (or −1E99), using the EE key.
- Inverse: menu → Probability → Distributions → Inverse Normal. Area 0.9, μ 50, σ 8. OK.
- Finding σ or μ: Inverse Normal with μ = 0 and σ = 1 gives z, then solve z = (x − μ) ÷ σ.
- Inverse Normal uses the area to the left.
For teachers: Show on the board Print a keystroke card Teaching GDC skills
Quick answers
How do I do inverse normal on the fx-CG50?
MENU → 2 (STATISTICS) → F5 (DIST) → F1 (NORM), then: Inverse: F3 (InvN). Tail: Left, Area 0.9, σ 8, μ 50, then Execute.
How do I do inverse normal on the TI-84 Plus CE?
Inverse: 2nd vars → 3: invNorm(. area: 0.9, μ: 50, σ: 8, Tail: LEFT (the Tail option is on OS 5.x). enter.
How do I do inverse normal on the TI-Nspire CX II?
Inverse: menu → Probability → Distributions → Inverse Normal. Area 0.9, μ 50, σ 8. OK.
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.
Now try it on an exam-style question
Use the keystrokes above on IB-style normal distribution questions. Free to try, no sign-up.
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.
- Writing "normalcdf(45, 60, 50, 8)" as your working: the IB wants mathematical notation, P(45 < X < 60) = 0.628.
- Accuracy: unless the question says otherwise, IB markschemes want answers exact or to 3 significant figures. Keep the full calculator value for later parts and round only the answer you write down (x = 2.094551… is written 2.09, not 2.1 or 2.0946).
If you get an error
fx-CG50: Ma ERROR
Ma ERROR Casio's Math ERROR: the result is outside the allowable calculation range, or you are trying to do an illegal mathematical operation, such as dividing by zero. Check: Is every value allowed? σ must be positive and p must be between 0 and 1. A value typed into the wrong box (σ where μ goes) can do it too. Fix: Casio's advice: check your input values and change them so the result is within the allowable range.
TI-84 Plus CE: ERR:DOMAIN, ERR:SYNTAX, ERR:ARGUMENT
ERR:DOMAIN A value given to a function or instruction is outside the values it accepts. In a regression, TI says it means the data do not suit the model you chose. Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Exponential and power models need positive data. Fix: Change the value that is out of range, or choose a model that suits the data.
ERR:SYNTAX The command contains a syntax error: a misplaced function, argument, bracket or comma. Check: TI points out that subtract − and negative (−) are different keys, and using the wrong one causes this error. Then check the brackets and commas. Fix: Find the misplaced function, argument, bracket or comma and correct it.
ERR:ARGUMENT A function or instruction does not have the correct number of arguments (inputs). Check: A distribution command with an input missing: normalcdf( needs lower, upper, μ and σ. Fix: Give every argument, separated by commas.
TI-Nspire CX II: Domain error, Syntax error, Too few arguments / Too many arguments
Domain error An argument must be in a specified domain, and this one is not (TI's example: rand(0)). Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Fix: Change the value that is out of range.
Syntax error The syntax checker found a problem. Check: A missing bracket or comma. Fix: Correct the expression and try again.
Too few arguments / Too many arguments The function or command was given fewer (or more) arguments than it needs. Check: A distribution or statistics command with a value missing or an extra comma. Fix: Give exactly the arguments the command needs.
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.
Open desmos.com/calculator (free, in any browser) and type:
N=normaldist(50,8)N.cdf(45,60)N.inversecdf(0.9)
Questions
Can I use a calculator for normal distribution in the exam?
In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well.
What are the fx-CG50 keystrokes for normal distribution?
MENU 2 (STATISTICS), then F5 (DIST) F1 (NORM). Then 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). Then One-sided: for P(X > 62) use Lower 62, Upper 1E99 (type 1 ×10ˣ 99); for P(X < k) use Lower −1E99. The full steps and the other calculators are in the keystrokes section above.
Does this work on other calculators?
Yes. This page has keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II. The worked example has the same answers on every model, so use it to check.
What should I write as working?
Write the maths, not the key presses: say what you are finding in normal notation (the equation, the probability statement or the integral), then the calculator's answer exact or to 3 significant figures unless the question says otherwise. Keep full accuracy in later parts.
How do I do inverse normal on the fx-CG50?
MENU → 2 (STATISTICS) → F5 (DIST) → F1 (NORM), then: Inverse: F3 (InvN). Tail: Left, Area 0.9, σ 8, μ 50, then Execute.
How do I do inverse normal on the TI-84 Plus CE?
Inverse: 2nd vars → 3: invNorm(. area: 0.9, μ: 50, σ: 8, Tail: LEFT (the Tail option is on OS 5.x). enter.
How do I do inverse normal on the TI-Nspire CX II?
Inverse: menu → Probability → Distributions → Inverse Normal. Area 0.9, μ 50, σ 8. OK.
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 models 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. A calculator with no tab here has no checked steps for this skill yet. Worked-example answers were recomputed independently in Python.