For a population that is not normally distributed, the distribution of the sample means will

If data are not normally distributed then there are only two tendencies for its distribution. It could either be skewed to right where most of the values are to the right of the mean.

Another tendency for the data is that they are skewed to the left. With this, most of the data are to the left of the mean.

Hence, the sample means also shifted depending on the skewness of the data.