  In this paper, we develop a simple non-parametric test for testing normal
distribution based on the distance between empirical zero-bias transformation
and empirical distribution. The asymptotic properties of the test statistic are
studied. The finite sample performance of the proposed test is evaluated
through a Monte Carlo simulation study. The power of our test is compared with
several other tests for normality. We illustrate the test procedure using two
real data sets. We also develop a jackknife empirical likelihood ratio test for
standard normal distribution.
