1. Confidence Intervals & Normal Distribution | Calculating a 90% confidence interval for the population mean of leaf lengths from a sample.

2. Probability Generating Functions | Finding variance from given probability generating functions and determining the function for the sum of independent variables.

3. Goodness of Fit Test & Binomial Distribution | Testing whether the number of germinated seeds follows a binomial distribution using a chi-squared test at a 10% significance level.

4. Probability Density Functions & Distributions | Deriving the cumulative distribution function, transforming variables, finding expected values, and calculating medians.

5. Hypothesis Testing & Mean Comparisons | Testing whether the mean juice volume from two machines significantly differs and determining the range of significance levels.

6. Wilcoxon Signed-Rank Test | Conducting a non-parametric test at a 5% significance level to assess whether intensive training has reduced student lap times.