Finding an x-value from a probability
- Quartiles
- The quartiles of a distribution are the three values such that there is probability 1/4, 2/4 and 3/4 of being lower.
- Percentiles
- The r'th percentile of the distribution is the value with probability r/100 of being lower.
- Quantiles
- These are generalised by the term quantile. The value with probability p of being lower is called the quantile of the distribution corresponding to probability p.
Finding quantiles
To find the x-value for which there is probability p of a normal distribution being lower,
- Find the z-score for which there is probability p of being less.
- Translate the z-score to an x-value
The first step of this process can be done with Excel (or other statistical software) or statistical tables can be used. For example, the
diagram below shows how to find the z-score such that there is probability
0.9 of being less.
Translating from a z-score to the corresponding x-value is done with the
formula,
x = μ + z σ