SPM 2017 Add Maths Paper 1, Question 25Probability Distribution

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Probability Distribution · 4:26 video

The question

Diagram 10 shows a standard normal distribution graph. The probability represented by the area of the shaded region is 0.2881. (a) Find the value of h. (b) X is a continuous random variable which is normally distributed with a mean, mu, and a variance of 16. Find the value of mu if the z-score of X = 58.8 is h.

[4 marks]

SPM 2017 Add Maths Paper 1, Question 25: the question as drawn in Eduly's video4:26

Step 1

The area from z = h to z = 0 is 0.2881. Since the area from z = -infinity to 0 is 0.5, the area from -infinity to h is P(Z<h) = 0.5 - 0.2881 = 0.2119.

Why this step

Half the curve (0.5) is left of 0 and the strip sits inside it, so subtract. Taking 0.2881 as P(Z < h) is the common mistake.

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

Final answer

h = −0.8, μ = 62

Where students lose marks

Watch out: the shaded strip is not P(Z < h). Subtract it from 0.5 first, otherwise h and then μ come out wrong.

Watch every step of this question solved on video (4:26), with the reason behind each step and a box that checks your own answer.

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