Melaka Trial 2025 Add Maths Paper 1, Question 15Probability Distribution

Solved on video in English · Form 5, Probability Distribution · 7:09 video

The question

(a)(i)

A workshop is conducting an inspection on newly installed batteries. Statistics show that 2 out of 5 batteries function well after one year. A random sample of n batteries is selected. It is given that the probability that all selected batteries function well after a year is 0.0256.

(a)(i) Find the value of n.

(a)(ii)

A workshop finds that 2 out of 5 batteries function well after one year, and a random sample of n = 4 batteries is selected.

(a)(ii) Find the probability that all the batteries do not function well after a year.

(b)(i)

(b)(i) If X ~ N(56, 16), find the value of P(X > 64).

(b)(ii)

Diagram 7 shows a standard normal distribution graph. The probability represented by the area of the shaded region is 36.65%.

(b)(ii) Find the value of k.

Melaka Trial 2025 Add Maths Paper 1, Question 15: the question as drawn in Eduly's video7:09

Part (a)(i)

Step 1

Probability a battery functions well p = 2/5 = 0.4. Using the binomial distribution, P(all n function well) = ⁿCₙ (0.4)ⁿ (0.6)⁰ = (0.4)ⁿ.

Why this step

Use 0.4 because we want batteries that work, not 0.6. All n must work, so ⁿCₙ = 1 and (0.6)⁰ = 1.

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

Final answer

n = 4

Where students lose marks

Watch out: use 0.4 (works well), not 0.6, and test values to see that (0.4)ⁿ = 0.0256 gives n = 4.

Part (a)(ii)

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

Final answer

0.1296

Where students lose marks

Watch out: 'does not function well' uses 0.6, not 0.4, and all 4 must fail, so the power is 4.

Part (b)(i)

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

Final answer

P(X > 64) = 0.0228

Where students lose marks

Watch out: N(56, 16) means variance 16, so divide by σ = 4, not 16, and read the correct tail of the table.

Part (b)(ii)

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

Final answer

k = −1.11

Where students lose marks

Watch out: use 0.5 − 0.3665 = 0.1335 for the tail, not 0.3665, and remember k is on the left, so it is negative.

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