How does this calculator help me?
This calculator can help if you have a z-score (z value) and you need to convert it to a percentage or a p-value.
Z-scores can be converted to probabilities with calculators. This is helpful if you want to know the probability that you got a certain value by random chance. If, for example, you are asked to calculate the probability that a randomly selected student got a score, and you’re told the population standard deviation, we can convert the score to a z-score and use this calculator to calculate the probability of obtaining such a value.
We want to use calculators or tables to convert z-scores to probabilities or to convert z-scores to percentiles because the formula for the normal distribution is relatively complicated. A complicated integral calculation would be needed to find the probability or p-value if it weren’t for this type of calculator or for a table of values.
The following is an example of a homework problem where students are asked to convert a z-score to a percentile.
If you have a number and you are asked to calculate the probability of randomly getting that number, and if you’re assured the data for this number is approximately normally distributed, then you can convert the number to a z-score and calculate the probability of that z-score.
If you’re not sure whether you should be using a z-score value or a t-value, you will want to look at the data you have available. A z-score should be used if you are assured that a data set is approximately normal, if you are conducting a hypothesis test about a proportion, or if you are conducting a hypothesis test about a mean and the population standard deviation is known. If you're conducting a hypothesis test about a mean, and your sample size is less than 30, and you don't know the population standard deviation, you probably want a t-to-percentile calculator.