MRSM Trial 2025 Add Maths Paper 1, Question 12Probability Distribution

Solved on video in English · Form 5, Probability Distribution · 6:06 video

The question

(a)

Given a discrete random variable X ~ B(7, 2/3), find the variance of the distribution.

(b)

Diagram 4 shows a normal distribution graph for the travel time, in minutes, taken by passengers from station P to station Q. The shaded region (to the left of x = 22.41) represents 16% of the total area under the graph and the mean is 17 times the standard deviation. Find the standard deviation.

MRSM Trial 2025 Add Maths Paper 1, Question 12: the question as drawn in Eduly's video6:06

Part (a)

Step 1

For a binomial distribution, variance = npq where n = 7, p = 2/3, q = 1 − 2/3 = 1/3.

Why this step

Variance measures spread, so we use npq, not np (that is the mean). Work out q = 1 − p first so nothing gets forgotten.

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

Final answer

Variance = 14/9 ≈ 1.556

Where students lose marks

Watch out: variance is npq, not np (that is the mean). Work out q = 1 − p first.

Part (b)

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

Final answer

σ = 1.400

Where students lose marks

Watch out: a left tail below 0.5 gives a negative z. Substitute μ = 17σ, then collect σ terms carefully: 17σ − 0.994σ.

Watch every step of this question solved on video (6:06), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in MRSM Trial 2025 Paper 1

Probability Distribution: lessons and every past-year question

More Probability Distribution questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.