No need for z-tables or standardising - the GDC works straight from μ and σ.
In short: Normal distribution probabilities give the chance that a normally distributed variable falls in a range, found with the normal cumulative distribution function (normalcdf or Ncd). You enter the lower bound, the upper bound, the mean and the standard deviation. Use it for questions such as P(a < X < b), and sketch the curve first.
When you'd use this
A quantity is described as "normally distributed" with a given mean and standard deviation.
Finding P(a < X < b), or P(X > a), for a continuous normal variable.
Avoiding the standardising-then-z-table method entirely - the GDC works directly from μ and σ.
Checking a probability you estimated using the 68-95-99.7 rule.
Here's a real IB-style question that uses exactly this technique.
MediumCalculatorPaper 2[3 marks]
The random variable X ~ N(50, 8²). Find P(45 < X < 60), to 3 significant figures.
0.628
Mark it
Correct3 / 3 marks
Worked solution & mark scheme:
M1 normalcdf(45, 60, 50, 8)
A1 0.628
Common questions
When would I need to find normal distribution probabilities in IB Maths?
No need for z-tables or standardising - the GDC works straight from μ and σ. A quantity is described as "normally distributed" with a given mean and standard deviation. Finding P(a < X < b), or P(X > a), for a continuous normal variable.
How do I find normal distribution probabilities on a TI-84 Plus CE?
1. Decide what you need: P(a < X < b), a tail, or a value from a probability. 2. 2nd → DISTR → normalcdf(lower, upper, μ, σ). For inverse, invNorm(area-to-left, μ, σ). 3. For a left tail use a very small lower bound (e.g. −1E99); for a right tail use 1E99 as the upper bound.
How do I find normal distribution probabilities on a Casio fx-CG50 and fx-CG100?
1. Decide what you need: P(a < X < b), a tail, or a value from a probability. 2. Statistics menu → DIST (F5) → NORM (F1) → Ncd (or InvN for inverse). 3. For a left tail use a very small lower bound (e.g. −1E99); for a right tail use 1E99 as the upper bound.
How do I find normal distribution probabilities on a TI-Nspire CX?
1. Decide what you need: P(a < X < b), a tail, or a value from a probability. 2. menu → Statistics → Distributions → Normal Cdf (or Inverse Normal). 3. For a left tail use a very small lower bound (e.g. −1E99); for a right tail use 1E99 as the upper bound.
What should I watch out for when I find normal distribution probabilities?
Sketch the bell curve and shade the region first - it stops you mixing up 'less than' and 'greater than'. For "more than", use the lower bound and a very large upper bound (e.g. 1E99); for "less than", use a very negative lower bound.
How are marks awarded when I find normal distribution probabilities in an IB exam?
In the worked example on this page (3 marks, Paper 2), the marks are: M1: normalcdf(45, 60, 50, 8); A1: 0.628.
