You can check a normal distribution by means of normality tests such as the Shapiro-Wilk normality test, which is assumed to be the most accurate one for almost all small to large sample sizes. The Sig. value of this test should be less than 0.05 to claim that a data set is not normally distributed. Visually, you can also check the histogram and the normal Q-Q plot. Additionally, you can check the values of the skewness and kurtosis divided by their standard errors; if the value does not fall within ±1.96 for p < 0.05, ±2.58 for p < 0.01, and ±3.29 for p < 0.001, it can be concluded that the distribution is not normal.
Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486-489. https://dx.doi.org/10.5812%2Fijem.3505