Examples and practice
The normal distribution
Back to lessonPractice section 1 · Questions 1–6
Translate intervals and tails into normal probabilities · Practise interval, left-tail and central probabilities · +4 more
Practice section 2 · Questions 7–12
Find the range of distinction cutoffs · Use the standard normal model directly · +4 more
Practice section 3 · Questions 13–18
Scale one observation or combine independent variables · Distinguish two children from twice one child · +4 more
Practice section 4 · Questions 19–24
Use the lower-tail quantile to set the new filling mean · Convert both rejection rates into quantile equations · +4 more
- Use the lower-tail quantile to set the new filling mean
- Convert both rejection rates into quantile equations
- Locate the mean midway between equal normal tails
- Allow an interval endpoint on either side of the fixed bound
- Choose between scaling one value and adding independent values
- Distinguish six separate rods from three times one rod
Practice section 5 · Questions 25–30
Add a fixed box mass and retain both at-least-one methods · Separate contents, packaging and independent packet sums · +4 more
- Add a fixed box mass and retain both at-least-one methods
- Separate contents, packaging and independent packet sums
- Compare an intersection event with the larger total-price event
- Preserve the absolute deviation when relating two normal tails
- Keep the square-root growth in the large-sample tail
- Compare two runners and distinguish a sum from a multiple
Practice section 6 · Questions 31–36
Scale fruit masses before combining independent prices · Use the given variances and the central eighty percent · +4 more
- Scale fruit masses before combining independent prices
- Use the given variances and the central eighty percent
- Keep both tails of a call-duration difference and all handling fees
- Keep a strict probability condition strict at the quantile boundary
- Condition on the total length before interpreting two short pickles
- Find a central height interval and a large-sample tail limit
Practice section 7 · Questions 37–41
Recover a component normal distribution from a sum of two observations · Keep the instructed rounded model consistent with later probabilities · +3 more
- Recover a component normal distribution from a sum of two observations
- Keep the instructed rounded model consistent with later probabilities
- Interpret a probability inequality as a range of mass thresholds
- Square the coefficient of a two-packet total and retain both tails
- Maximise a normal interval probability by choosing its mean