Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 11Probability Distribution

Solved on video in English · Form 5, Probability Distribution · 7:01 video

The question

(a)

In a certain school, it is found that 40% of the students from a certain class obtained grade A in Additional Mathematics in the SPM trial examination.

(a) If 10 students from the class are selected at random, find the probability that at least 2 students obtained grade A.

(b)(i)

A study shows that the monthly salary of factory workers between the ages of 25 and 30 years is normally distributed as shown in Diagram 7, where AB is the axis of symmetry, the values 3000 and 3500 are marked on the x-axis, and the region to the right of 3500 is shaded and labelled 34.46%.

(b)(i) Find the mean, μ.

(b)(ii)

A study shows that the monthly salary of factory workers between the ages of 25 and 30 years is normally distributed as shown in Diagram 7 (AB is the axis of symmetry at 3000; the region to the right of 3500 is 34.46%).

(b)(ii) Find the standard deviation, σ.

(b)(iii)

A study shows that the monthly salary of factory workers between the ages of 25 and 30 years is normally distributed as shown in Diagram 7 (mean 3000, standard deviation 1250).

(b)(iii) If 10 000 workers are chosen at random, find the number of workers who have a monthly salary between RM3000 and RM3500.

Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 11: the question as drawn in Eduly's video7:01

Part (a)

Step 1

This is a binomial distribution with n = 10 and p = 0.4 (probability of grade A).

Why this step

10 fixed trials, each grade A or not. That's binomial, and p is the chance of what we count: grade A, so 0.4 (not 0.6).

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

Final answer

P(X ≥ 2) = 0.9536

Where students lose marks

Watch out: “at least 2” is P(X ≥ 2), not P(X = 2). Keep the “1 −” and use p = 0.4 (not 0.6).

Part (b)(i)

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

Final answer

μ = 3000

Where students lose marks

Watch out: the mean is at the axis of symmetry, 3000. It is not 3500, and not the midpoint of 3000 and 3500.

Part (b)(ii)

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

Final answer

σ = 1250

Where students lose marks

Watch out: 0.3446 is an upper-tail area, so z = 0.4 (positive). Don't treat it as a left-tail area.

Part (b)(iii)

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

Final answer

1554 workers

Where students lose marks

Watch out: the probability is 0.5 − 0.3446 = 0.1554, not 0.3446. Then multiply by 10 000, not 1000.

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