The normal distribution has several key properties: it is symmetric, with mean, median and mode equal; it has skewness of zero and kurtosis of zero. Approximately 68% of observations lie within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Confidence intervals for a mean provide a range that the population mean is likely to fall within, such as 95% being between the sample mean ± 1.96 standard deviations divided by the square root of the sample size. Statistical hypothesis testing involves setting a null and alternative hypothesis, choosing a significance level such as 0.05, determining the test statistic and degrees of freedom, and deciding whether to reject the