Z-score and normal probability calculator

Enter your values. The answer and the full worked solution update as you type.

Result

z-score1.333
P(X < x)0.9088
P(X > x)0.09121
Percentile90.88 %

Step-by-step solution

Standardise

z = (x − μ)/σ = (120 − 100)/15 = 1.333

Areas

P(X < x) = Φ(1.333) = 0.9088
P(X > x) = 1 − Φ(z) = 0.09121

Key formulas

z-score
z = (x − μ)/σ
Below x
P(X < x) = Φ(z)
Above x
P(X > x) = 1 − Φ(z)
Between
Φ(z2) − Φ(z1)
Percentile
x = μ + z·σ

Practise Normal distribution

A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.

Practise Normal distribution for freePractise Normal distribution nowWorked examples
</> Embed

Free for teachers and schools: paste this code into your course page, LMS or website. Students can use the calculator and its worked solution without an account.

More calculators

Confidence interval calculatorSample size calculatorMean, median and standard deviation calculatorLinear regression calculatorChi-square goodness-of-fit calculatorMatrix determinant and inverse calculatorNormal distribution calculatorBinomial distribution calculatorPoisson distribution calculatorPermutation and combination calculator (nPr and nCr)