SPM 2019 Add Maths Paper 1, Question 25Probability Distribution

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Probability Distribution · 6:07 video

The question

Diagram 11 shows the normal distribution graph of the time for a school bus to arrive at a school. The area between 2 minutes below the mean and the mean is 25%, and the area between the mean and 2 minutes above the mean is 25% (so together they cover 50%), while the two outer tails beyond mean-2 minutes and beyond mean+2 minutes each cover the remaining 25%. (a) Find the standard deviation. (b) It is given that the mean time for the bus to arrive at the school is 7.15 a.m. Students are considered late if they arrive after 7.20 a.m. Lea takes that bus to school. Calculate the probability that Lea will be late. Give your answer correct to three significant figures.

[4 marks]

SPM 2019 Add Maths Paper 1, Question 25: the question as drawn in Eduly's video6:07

Step 1

The area to the right of mu+2 is 25% = 0.25, so P(X > mu+2) = 0.25, i.e. P(Z > 2/sigma) = 0.25.

Why this step

The diagram splits the area into four equal parts, so the tail beyond μ + 2 is 25%. Standardising cancels μ, leaving 2/σ.

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

Final answer

(a) σ = 2.9674 minutes; (b) P(late) = 0.0460

Where students lose marks

Watch out: match the 25% tail to the right z-value, and convert the clock times into a 5-minute gap.

Watch every step of this question solved on video (6:07), with the reason behind each step and a box that checks your own answer.

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