Selangor Trial 2025 Add Maths Paper 2, Question 11Probability Distribution

Solved on video in English · Form 5, Probability Distribution · 7:36 video

The question

(a)(i)

(a) The probability that a student cycles to school is p. A sample of 5 pupils is randomly selected from the school. (i) If the probability of all 5 students cycling to school is 0.07776, find the value of p.

(a)(ii)

(a)(ii) Calculate the mean.

(a)(iii)

(a)(iii) Find the probability that more than 3 students cycle to school.

(b)

(b) The score of 150 students is normally distributed with a mean of 52 marks and a standard deviation of 30 marks. If the passing score is at least 40 marks, determine the number of students who failed.

Selangor Trial 2025 Add Maths Paper 2, Question 11: the question as drawn in Eduly's video7:36

Part (a)(i)

Step 1

Let X be the number of the 5 students who cycle; X follows a binomial distribution with n = 5 and probability p.

Why this step

Each of the 5 students either cycles or not, independently, with the same p. That fixed number of yes/no trials is exactly what makes it binomial.

3 more steps, each with the reason for it, in the full solution

Final answer

p = 0.6

Where students lose marks

Watch out: all 5 cycling gives just p⁵, with no factor of 5. Then take the fifth root carefully.

Part (a)(ii)

2 more steps, each with the reason for it, in the full solution

Final answer

mean = 3

Where students lose marks

Watch out: the mean is np. Don't use np(1 − p), that is the variance.

Part (a)(iii)

4 more steps, each with the reason for it, in the full solution

Final answer

P(X > 3) ≈ 0.3370 (1053/3125)

Where students lose marks

Watch out: 'more than 3' excludes X = 3, and don't forget the ⁵C₄ factor in P(X = 4).

Part (b)

4 more steps, each with the reason for it, in the full solution

Final answer

51 students

Where students lose marks

Watch out: failing is the lower tail P(Z < −0.4), and the number of students must be a whole number, not 51.69.

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