SPM 2021 Add Maths Paper 2, Question 11Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 9:37 video

The question

(a)

(a) A company produces a type of potato chips and packs them before marketing. A packet with mass from 75 g to 80 g is accepted for marketing, while a packet with mass out of that range is sent for repacking. Table 2 shows the mass of a packet of chips and the number of packets in ratio at a particular time: mass x < 75 → ratio 1; 75 ≤ x ≤ 80 → ratio 97; x > 80 → ratio 2. (a)(i) Find the mean number of packets of chips marketed if the company produces 5000 packets. (a)(ii) If 6 packets of chips are chosen at random from the company, find the probability that exactly 2 packets will be sent for repacking. (a)(iii) If a manager chooses 10 packets randomly from the repacking unit, find the probability that he will get more than 2 packets of chips that have a mass below the range.

(b)

(b) A random variable X is normally distributed with X ~ N(12, 25). Given that P(X > k) = (1/4) P(X ≤ k), find the value of k.

SPM 2021 Add Maths Paper 2, Question 11: the question as drawn in Eduly's video9:37

Part (a)

Step 1

Marketed packets are those with 75 ≤ x ≤ 80, with probability p = 97/(1 + 97 + 2) = 97/100.

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

Final answer

(i) 4850 packets; (ii) 0.01195; (iii) 0.7009

Where students lose marks

Watch out: the mean of a binomial is np, not npq. In (iii), use p = 1/3 inside the repacking unit, not 0.01.

Part (b)

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

Final answer

k = 16.21

Where students lose marks

Watch out: for P(X > k) = 0.2 the table gives z = 0.842. A wrong z-value like 2.046 gives a wrong k.

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