SPM 2020 Add Maths Paper 2, Question 7Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 8:13 video

The question

(a)(i)

In a residential area, it is found that the probability that a family owns a motorcycle is p. The number of families who own a motorcycle has a mean of 60 and a standard deviation of 6. (a)(i) Find the value of p.

(a)(ii)

(Using p = 0.4 from part (a)(i).) (a)(ii) If 10 families are selected at random, find the probability that 3 families own a motorcycle.

(b)

The length of pencils produced by a factory follows a normal distribution with a mean of mu and a standard deviation of sigma. If a pencil is chosen at random, the probability that its length is more than 19 cm is 0.2025, while the probability that its length is more than 16 cm is 0.9522. (b) Calculate the value of mu and of sigma.

SPM 2020 Add Maths Paper 2, Question 7: the question as drawn in Eduly's video8:13

Part (a)(i)

Step 1

Binomial distribution: mean = np = 60, and standard deviation = sqrt(npq) = 6, so variance npq = 36.

Why this step

Two unknowns, n and p, so we need both formulas together. Don't guess n = 6; use the mean and the standard deviation.

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

Final answer

p = 0.4 (= 2/5)

Where students lose marks

Watch out: don't guess n = 6. Use both the mean np = 60 and √(npq) = 6 together to find p.

Part (a)(ii)

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

Final answer

P(X = 3) ≈ 0.2150

Part (b)

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

Final answer

μ = 18, σ = 1.2

Where students lose marks

Watch out: never use the probabilities as z-scores, and for 0.9522 > 0.5 the z-value is negative. Sketch the curve to check.

Watch every step of this question solved on video (8:13), with the reason behind each step and a box that checks your own answer.

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