SPM 2016 Additional Mathematics (Forecast Paper)


SPM 2016 Additional Mathematics (Forecast Paper)

Section B
[40 marks]
Answer any four questions from this section.

Question 10
(a)    20% of the students in SMK Bukit Bintang are cycling to school. If 9 pupils from the school are chosen at random, calculate the probability that
            (i)     exactly 3 of them are cycling to school,
            (ii)   at least a student is cycling to school.                                                            
[4 marks]
(b)   The volume of 800 bottles of fresh milk produced by a factory follows a normal distribution with a mean of 520 ml per bottle and variance of 1600 ml2.
            (i)     Find the probability that a bottle of fresh milk chosen in random has a volume of less than        515 ml.
            (ii)   If 480 bottles out of 800 bottles of the fresh milk have volume greater that k ml, find the value of k.

[6 marks]
Answer and Solution:
(a)(i)
X ~ Students in SMK Bukit Bintang who are cycling to school
X ~ B (n, p)
X ~ B (9, 0.2)
P (X = r) = nCr. pr. qn-r
Probability, exactly 3 students are cycling to school
P (X = 3) = 9C3 (0.2)3 (0.8)6
            = 0.1761

(a)(ii)
At least a student is cycling to school
= 1 – P(X = 0)
= 1 – 9C0 (0.2)0 (0.8)9
= 0.8658

(b)(i)
m = 520 ml
σ2 = 1600 ml2
σ = 40
Let X represents volume of a bottle of fresh milk.
X ~ N (520, 1600)

P(X < 515)
=P( Z< 515520 40 )
= P(Z < – 0.125)
= P(Z > 0.125)
= 0.4502

(b)(ii)
P( X>k )= 480 800 P( Z> k520 40 )=0.6 k520 40 =0.253 k520=10.12 k=509.88