Examples and practice
The binomial distribution
Back to lessonPractice section 1 · Questions 1–6
Decide whether an experiment has a binomial model · Translate left-handedness counts into binomial probabilities · +4 more
- Decide whether an experiment has a binomial model
- Translate left-handedness counts into binomial probabilities
- Practise equality, tails and a centred absolute inequality
- Count qualifying chocolates, then qualifying boxes
- Find the largest sample meeting a strict probability bound
- Find the smallest battery sample below a probability bound
Practice section 2 · Questions 7–12
Find the least integer threshold for late days · Write an equation before solving for a game probability · +4 more
- Find the least integer threshold for late days
- Write an equation before solving for a game probability
- Model red cars and solve a zero-or-one probability
- Find a probability within one standard deviation of a binomial mean
- Find one mode or two exactly tied modes
- Use a unique mode to bound p, then sketch a different distribution
Practice section 3 · Questions 13–18
Translate five burger events into probabilities · A specified success position and a remaining tail · +4 more
Practice section 4 · Questions 19–24
Convert the hit count into a score · Game winnings, a mode and a tournament cutoff · +4 more
Practice section 5 · Questions 25–30
Distinguish a sample count from the position of a final success · Count faults across two boxes rather than test each box separately · +4 more
- Distinguish a sample count from the position of a final success
- Count faults across two boxes rather than test each box separately
- Solve a rejection probability and then model accepted cartons
- Compare a binomial majority with waiting for one further red pen
- Carry a rare cap-defect tail into a box-level distribution
- Carry an underweight-chocolate event into a box count
Practice section 6 · Questions 31–36
Translate birthday counts and find a strict minimum sample size · Derive a cookie success rate and compare two minimum-packet methods · +4 more
- Translate birthday counts and find a strict minimum sample size
- Derive a cookie success rate and compare two minimum-packet methods
- Convert weeks to trials and use a variance restriction
- Read a binomial mode and an expected number of qualifying samples
- Use a noninteger mean, compare modal counts and audit finite-population assumptions
- Find the smallest binomial distribution with two tied modes
Practice section 7 · Questions 37–40
Choose hypergeometric or binomial sampling from replacement rules · Compare an ordered third success with exactly three successes · +2 more