SPM 2023 Add Maths Paper 2, Question 9Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 8:17 video

The question

(a)

It is found that 75% of the students in SMK Permai go to school by bus. If 8 students are chosen at random from the school, find the probability that at most 2 of them do not go to school by bus.

(b)(i)

The mass of fish reared in a pond is normally distributed with a mean of 1.5 kg and a standard deviation of 0.4 kg. The fish are graded by mass as shown in Table 1, where k is a constant: x < k → Grade C; k ≤ x ≤ 2 → Grade B; x > 2 → Grade A.

(b)(i) A fish is caught at random from the pond. Find the probability that it is of grade A.

(b)(ii)

The mass of fish is normally distributed with mean 1.5 kg and standard deviation 0.4 kg; grades: x < k → C, k ≤ x ≤ 2 → B, x > 2 → A.

(b)(ii) It is given that 72.84% of the fish in the pond are of grade B. Represent the situation by sketching the standard normal distribution graph and express the shaded region in probability notation. Hence, find the value of k.

SPM 2023 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video8:17

Part (a)

Step 1

Let X = number of the 8 students who do NOT go by bus. P(not by bus) = 1 − 0.75 = 0.25, so X ~ B(8, 0.25).

Why this step

We count the students who do NOT go by bus, so p = 0.25, not 0.75. Misreading this is a common way to lose marks.

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

Final answer

P(X ≤ 2) = 0.6785

Where students lose marks

Watch out: p = 0.25 for NOT going by bus, not 0.75. 'At most 2' means add X = 0, 1 and 2.

Part (b)(i)

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

Final answer

P(grade A) = 0.1056

Where students lose marks

Watch out: read the table carefully. The value for z = 1.25 is 0.1056, and a neighbouring entry like 0.1057 loses the mark.

Part (b)(ii)

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

Final answer

k = 1.112

Where students lose marks

Watch out: sketch and shade the region correctly, and check the sign. Area 0.1660 is below 0.5, so z = −0.97, not +0.97.

Watch every step of this question solved on video (8:17), 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 2023 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.