IB · Mathematics: Applications & Interpretation SL & HL · Statistics & probability

Binomial & normal distributions: IB Mathematics: Applications & Interpretation questions with answers

Free Binomial & normal distributions questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.

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Binomial & normal distributions practice questions

Question 1Structured · 7 marksA* challenge

The volume of drink in a bottle is normally distributed with mean 80 ml. 15% of bottles contain more than 87.5 ml.

(a)

Find the standard deviation.

[3]
(b)

Find the probability that a bottle contains less than 76.25 ml.

[2]
(c)

Ten bottles are chosen at random. Find the probability that at least two contain less than this volume.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)7.24
z = 1.04 (A1)
1.04 = (87.5 − 80)/σ (M1)
σ = 7.24 A1
3
(b)0.302
normalcdf with their σ (M1)
0.302 A1
2
(c)0.854
B(10, p) and 1 − P(X ≤ 1) (M1)
0.854 A1
2
Question 2Structured · 6 marksA* challenge

The masses of loaves are normally distributed with mean 250 g. 10.6% of loaves have mass greater than 265 g.

(a)

Find the standard deviation of the masses.

[3]
(b)

Find the least number of loaves that must be chosen so that the probability that at least one has mass greater than 265 g is more than 0.95.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)12.0 g
P(X > 265) = 0.106 (M1)
z = 1.25 (A1)
σ = 12.0 g A1
3
(b)27
1 − (1 − 0.106)n > 0.95 (M1)
solving (M1)
27 A1
3
Question 3Structured · 4 marks

The masses of apples are normally distributed with mean 75 g and standard deviation 5 g.

(a)

Find the probability that an apple has mass between 70 g and 85 g.

[2]
(b)

Find the mass exceeded by 10% of apples.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.819
GDC normalcdf (M1)
0.819 A1
2
(b)81.4 g
inverse normal (M1)
81.4 A1
2
Question 4Structured · 6 marks

The probability that a seed germinates is 0.3. A packet contains 12 seeds.

(a)

Find the probability that exactly 4 seeds germinate.

[2]
(b)

Find the probability that more than 4 seeds germinate.

[2]
(c)

Find the expected number and the variance of the number of seeds that germinate.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.231
B(12, 0.3) (M1)
0.231 A1
2
(b)0.276
1 − P(X ≤ 4) (M1)
0.276 A1
2
(c)3.6, 2.52
E = 3.6 A1
Var = 2.52 A1
2
Question 5Structured · 5 marks

The lengths of a species of fish are normally distributed with mean 65 mm and standard deviation 12 mm.

(a)

Find the probability that a fish is longer than 79.4 mm.

[2]
(b)

10 fish are caught. Find the probability that exactly 2 are longer than 79.4 mm.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.115
normal CDF (M1)
0.115 A1
2
(b)0.224
X ~ B(10, 0.115) (M1)(A1)
0.224 A1
3
Question 6Structured · 7 marksA* challenge

The volume of drink in a bottle is normally distributed with mean 80 ml. 10% of bottles contain more than 90 ml.

(a)

Find the standard deviation.

[3]
(b)

Find the probability that a bottle contains less than 75 ml.

[2]
(c)

Ten bottles are chosen at random. Find the probability that at least two contain less than this volume.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)7.80
z = 1.28 (A1)
1.28 = (90 − 80)/σ (M1)
σ = 7.80 A1
3
(b)0.261
normalcdf with their σ (M1)
0.261 A1
2
(c)0.780
B(10, p) and 1 − P(X ≤ 1) (M1)
0.780 A1
2

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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