Probability — popular questions

The hardest part of a statistics problem is usually picking the right test — t-test or z-test, one-sample or two-sample, paired or independent. Acemy's statistics catalog leads with that decision: the first paragraph of every answer states which test applies and why (sample size, known variance, paired structure). Probability problems explicitly state the sample space before counting; distribution problems name the distribution before computing.

Type I / Type II error tradeoffs are surfaced when relevant. Confidence intervals include the margin-of-error calculation, not just the final interval. Where a problem could be solved with either a normal approximation or an exact distribution, both paths are noted with the cutoff (np ≥ 10) that determines which is appropriate.

Write down the test you'd use before checking the answer. Half the work of a statistics problem is in that decision; the rest is plug-and-chug. The variant problem usually changes the sample size or assumption (known vs. unknown variance), which flips the appropriate test — that's the pattern to learn.