The Normal Distribution — Drills
The Normal Distribution has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 7 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Percent — Parts per hundred. 37% = 37100 = 0.37.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Standard deviation — A measure of typical distance from the mean.
- z-score — How many standard deviations a value sits from the mean: z = x - μσ.
- Empirical rule — About 68%, 95% and 99.7% lie within one, two and three deviations.
- Percentile — The percentage of the population at or below a value.
- Height — The perpendicular distance from the base to the opposite corner.
Zscore
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A population is normal with mean 50 and standard deviation 20. Find the z-score of 70.
Worked answer
1
70-5020=1
Problem 2
A population is normal with mean 100 and standard deviation 15. Find the z-score of 55.
Worked answer
-3
55-10015=-3
Value
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Mean 170, standard deviation 15. What value is 3 deviations above the mean?
Worked answer
215
170 + 3(15) = 215
Problem 2
Mean 500, standard deviation 10. What value is 1 deviation below the mean?
Worked answer
490
500 - 1(10) = 490
Interval
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Mean 170, deviation 10. What percent of the population lies between 140 and 200?
Worked answer
99.7
That is μ ± 3σ
About 99.7%
Problem 2
Mean 500, deviation 10. What percent of the population lies between 480 and 520?
Worked answer
95
That is μ ± 2σ
About 95%
Tail
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Mean 500, deviation 15. What percent of the population is above 515?
Worked answer
16
32% lies outside 1 deviation
Half of that is above: 16%
Problem 2
Mean 50, deviation 10. What percent of the population is above 70?
Worked answer
2.5
5% lies outside 2 deviations
Half of that is above: 2.5%
Counting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
In a group of 400 with normally distributed scores, about how many lie within one standard deviation of the mean?
Worked answer
272
0.68 × 400 = 272
Problem 2
In a group of 500 with normally distributed scores, about how many lie within one standard deviation of the mean?
Worked answer
340
0.68 × 500 = 340