SPM 2023 Add Maths Paper 1, Question 12Probability Distribution

Solved on video in English and Bahasa Melayu · 1 marks · Form 5, Probability Distribution · 5:56 video

The question

(a)

A farm produces strawberries. The masses of the strawberries, x grams, are normally distributed such that X ~ N[20, (0.5)²]. (a) State the mean and the variance of the distribution.

[1 marks]

(b)(i)

Diagram 8 shows the standard normal distribution graph for the mass of the strawberries. The shaded region represents the probability that the mass of the strawberries is between (−α + 40) grams and α grams. (b)(i) If the shaded region represents P(|Z| < k), express m in terms of α.

(b)(ii)

Using the same distribution X ~ N[20, (0.5)²] and Diagram 8, find the value of α when P(|Z| < k) = 0.2662, where k = (α − 20)/0.5.

SPM 2023 Add Maths Paper 1, Question 12: the question as drawn in Eduly's video5:56

Part (a)

Step 1

For X ~ N[μ, σ²], the mean is μ = 20.

1 more step, with the reason for it, in the full solution

Final answer

Mean = 20, variance = 0.25

Where students lose marks

Watch out: 0.5 is the standard deviation. The variance is (0.5)² = 0.25, so square it.

Part (b)(i)

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

Final answer

m = −2α + 40

Where students lose marks

Watch out: the numerator is −α + 20, not −(α + 20). Keep the sign of α, then divide every term by 0.5.

Part (b)(ii)

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

Final answer

α = 20.17

Where students lose marks

Watch out: convert P(|Z| < k) = 0.2662 to a tail probability first, 1 − 2P(Z ≥ k), before reading the Z-table.

Watch every step of this question solved on video (5:56), 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 1

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.