The step-by-step z-score calculator calculates a z-score based on the z-score formula. First, enter values for the mean, standard deviation, and data value. The calculator will then give you an answer, and guide you through a solution so you can learn to solve this problem on your own.

See also What is a Z-Score? and Z-Score Formula.

### Answer: -1.65

### Solution:

Depending on what your distribution represents, start by either writing the formula for the z-score of a population: $$z = {{x-{\mu}} \over {\sigma}}$$

or the formula for the z-score of a sample: $$z = {{x-{\bar{x}}} \over s}$$

Substitute in values for this problem (data value, mean, and standard deviation) into the formula: $$z = {{145 - 178} \over 20}$$

If you are using a calculator, make sure you put the numerator in parentheses to ensure it is evaluated first. Here, we round the answer to 2 decimal places.
$$z = \frac{(145 - 178)}{20}$$
$$z = -1.65$$