SPM 2022 Add Maths Paper 1, Question 8Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 5:13 video

The question

(a)

8 (a) Diagram 3 shows the standard normal distribution graph. On Diagram 3, shade the region(s) to represent P(|Z| ≥ a).

(b)(i)

8 (b) Diagram 4 shows the standard normal distribution graph which is divided into three equal parts A, B and C, with boundaries at z = −k and z = k (A is the left tail z < −k, B is the middle −k < z < k, C is the right tail z > k). State (i) the value of k.

(b)(ii)

8 (b)(ii) Using the division in Diagram 4 (with k = 0.431), state the mode for part A.

SPM 2022 Add Maths Paper 1, Question 8: the question as drawn in Eduly's video5:13

Part (a)

Step 1

P(|Z| ≥ a) means |Z| ≥ a, i.e. Z ≤ −a or Z ≥ a.

Why this step

The bars ignore the sign, so Z can be far below 0 or far above 0. Don't shade only one tail, that's the common slip.

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

Final answer

Shade both tails: Z ≤ −a and Z ≥ a

Where students lose marks

Watch out: |Z| ≥ a needs BOTH tails, left of −a and right of a. Shading only one is a common slip.

Part (b)(i)

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

Final answer

k = 0.431

Where students lose marks

Watch out: k is a z-score read from the table, not a probability. Do not write k = 1/3.

Part (b)(ii)

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

Final answer

mode = −0.431

Where students lose marks

Watch out: the mode is a z-value (the highest point in region A), not a probability. Do not write P(Z ≤ −0.431).

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