Other Uses of Z-test

Z-test can also be used to test hypotheses regarding populations other than normal because of the Central Limit Theorem.
Central Limit Theorem (CLT) states that any test statistic can be approximately normally distributed for large samples. Using CLT we can approximate any test statistic as a normal variable and use the Z-test to perform the hypothesis test.
This test is also used for testing the maximum likelihood estimators for the parameters in statistical models with parametric approach.
In nonparametric tests, sometimes the test statistic in Mann -Whitney U test can be approximated using normal distribution and Z-test is used thereby.