SPM 2022 Add Maths Paper 2, Question 9Probability Distribution

Solved on video in English and Bahasa Melayu · 5 marks · Form 5, Probability Distribution · 7:46 video

The question

(a)

The mass of police cadet members in a school is normally distributed with a mean of 60 kg. It is given that the probability that a police cadet member chosen at random from the school has a mass less than 61 kg is 0.9772.

(a) If 8 police cadet members are chosen at random from the school, find the probability that (i) all 8 members have the mass less than 61 kg, (ii) at most 6 members have the mass less than 61 kg.

(b)

Using the distribution of the mass of the police cadet members (normal, mean 60 kg, with P(mass < 61 kg) = 0.9772):

(b) If a police cadet member is chosen at random from the school, find the probability that the mass is less than 60.5 kg.

[5 marks]

SPM 2022 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video7:46

Part (a)

Step 1

This is a binomial distribution with p = P(mass < 61 kg) = 0.9772, q = 1 − p = 0.0228, n = 8, using P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ.

Why this step

Each member is either below 61 kg or not, with the same chance 0.9772 every time. That's what makes it a binomial experiment with n = 8.

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

Final answer

(i) 0.8315, (ii) 0.0133

Where students lose marks

Watch out: in (a)(i), write the full binomial formula ⁿCᵣ pʳ qⁿ⁻ʳ, not just the final number, or marks are lost.

Part (b)

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

Final answer

P(X < 60.5) = 0.8413 (σ = 0.5 kg)

Where students lose marks

Watch out: P(Z < 1) is the area to the left, so it's 1 − 0.1587 = 0.8413, not 0.1587.

Watch every step of this question solved on video (7:46), 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 SPM 2022 Paper 2

Probability Distribution: lessons and every past-year question

Baca dalam Bahasa Melayu

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.