Linear Combinations of Independent Normal Variables

Build practical skill in linear combinations of independent normal variables. This 25-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Standard normal probabilities and variance rules. Practice includes apply exact normal closure under independence; compute sums and differences of means and variances; analyze weighted combinations and averages; calculate comparison and exceedance probabilities; distinguish shared noise from independent copies; optimize precision and diagnose dependence assumptions. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.