Free Normal distribution questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.
Generate a full Normal Distribution worksheet →All Statistics & probability questionsThe heights of plants are normally distributed with mean 100 cm and standard deviation 10 cm.
Find the probability that a plant is taller than 110 cm.
Given that a plant is taller than 110 cm, find the probability that it is taller than 115 cm.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.159 normal CDF (M1) 0.159 A1 | 2 |
| (b) | 0.421 P(X > 115)P(X > 110) (M1) 0.06680.159 (A1) 0.421 A1 | 3 |
The volumes of bottles filled by a machine are normally distributed with mean 250 ml and standard deviation 8 ml.
Find the probability that a randomly chosen bottle has volume less than 256.4 ml.
Find the probability that a bottle has volume between 246 ml and 262 ml.
5% of bottles have volume greater than k ml. Find k.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.788 normal CDF with correct parameters (M1) 0.788 A1 | 2 |
| (b) | 0.625 normal CDF (M1) 0.625 A1 | 2 |
| (c) | 263 P(X > k) = 0.05, inverse normal (M1) 263 A1 | 2 |
The masses of apples from an orchard are normally distributed with mean 180 g and standard deviation 18 g. An apple is classified as large if its mass is greater than 200 g.
Find the probability that a randomly chosen apple is large.
Find the probability that an apple has a mass between 165 g and 200 g.
The lightest 20% of apples are used for juice. Find the maximum mass of an apple that is used for juice.
A bag contains 10 apples chosen at random. Find the probability that at least 2 of them are large.
Given that an apple has a mass greater than 180 g, find the probability that it is large.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.133 normal CDF (M1) 0.133 A1 | 2 |
| (b) | 0.664 normal CDF (M1) 0.664 A1 | 2 |
| (c) | 165 g P(X < k) = 0.2 (M1) inverse normal (M1) 165 g A1 | 3 |
| (d) | 0.393 Y ~ B(10, 0.133) (M1)(A1) 1 − P(Y ≤ 1) (M1) 0.393 A1 | 4 |
| (e) | 0.267 P(X > 200)P(X > 180) (M1) 0.1330.5 (A1) 0.267 A1 | 3 |
A random variable X is normally distributed with mean μ and standard deviation σ. P(X < 146.2) = 0.1 and P(X > 152) = 0.25.
Find the value of μ and the value of σ.
| Part | Answer and marking points | Marks |
|---|---|---|
| μ = 150, σ = 2.97 attempt to standardise (M1) 146.2 − μσ = −1.282 A1 152 − μσ = 0.6745 A1 attempt to solve simultaneously (M1) μ = 150 A1 σ = 2.97 A1 | 6 |
The heights of plants are normally distributed with mean 60 cm and standard deviation 10 cm.
Find the probability that a plant is taller than 70 cm.
Given that a plant is taller than 70 cm, find the probability that it is taller than 80 cm.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.159 normal CDF (M1) 0.159 A1 | 2 |
| (b) | 0.143 P(X > 80)P(X > 70) (M1) 0.02280.159 (A1) 0.143 A1 | 3 |
The masses of bottles filled by a machine are normally distributed with mean 50 g and standard deviation 4 g.
Find the probability that a randomly chosen bottle has mass less than 55.2 g.
Find the probability that a bottle has mass between 48 g and 58 g.
10% of bottles have mass greater than k g. Find k.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.903 normal CDF with correct parameters (M1) 0.903 A1 | 2 |
| (b) | 0.669 normal CDF (M1) 0.669 A1 | 2 |
| (c) | 55.1 P(X > k) = 0.1, inverse normal (M1) 55.1 A1 | 2 |
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in