Normal distribution on your calculator: normal cdf and inverse normal

Choose your calculator

The page remembers your choice on the other guides.

Check your own numbers

Type the values from your question. You get the keys with your numbers in them, the shaded picture to copy onto the paper, and the value to check against your screen.

Where the marks go, on any calculator

• Using the inverse command with the wrong tail. Draw the curve, shade the region, and write the area to the left before touching the calculator.
• Rounding too early. Keep the calculator value to at least 5 significant figures, round only the final answer to 3 s.f. (or to what the question asks).
• Confusing $P(X < a)$ with $P(X \le a)$. For a continuous variable they are the same: no correction is needed, unlike the binomial.
• Forgetting that a normal probability question may require the standardised value $z$ in a later part. If the question says "find $z$", the GDC answer for $x$ is not enough: $z = (x - \mu)/\sigma$.

What to write on the paper

1. State the distribution: $X \sim N(170, 8^2)$. The variance is written, not the standard deviation.
2. Write the probability you are computing in notation: $P(X > 180)$. This earns the method mark even if the calculator value is then wrong.
3. Write the calculator result to at least 4 s.f. before the rounded answer: 0.10565, so 0.106.
4. Do not write the calculator syntax (normCdf(...)) as working. Examiners accept it, but notation is safer and shows understanding.

Questions students ask

What do I type for infinity on the calculator?

On the TI-Nspire the default upper bound is 9E999, which is as large as the machine can represent. On the Casio fx-CG50 and TI-84 use 1E99 (1 then EXP or EE then 99). Any number ten standard deviations away from the mean gives the same answer to 3 s.f., but using the exponent form avoids thinking about it.

Why does my Casio give a different answer from my friend's TI?

Almost always because the Casio takes σ before μ and the Texas takes μ before σ. Check the argument order on the screen: on the Casio the dialog labels them, on the TI the pasted command shows them in brackets.

Does the IB accept the GDC answer without working?

For a direct probability yes, if you write the notation ($P(X < 180)$) and the answer to the required accuracy. Writing the calculator command alone is accepted but earns nothing extra. For questions that ask for $z$ values or for an unknown μ or σ, working is required.

How do I find μ or σ when they are unknown?

The GDC cannot do that directly with a normal cdf. Use invNorm on the standard normal (μ = 0, σ = 1) to get the $z$ value for the given probability, then solve $z = (x - \mu)/\sigma$ by hand or with the equation solver. With two unknowns you get two equations.