SPM Additional Mathematics (Model Test Paper)

SPM Additional Mathematics (Model Test 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]
(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)
$=P\left(Z<\frac{515-520}{40}\right)$
= P(Z < – 0.125)
= P(Z > 0.125)
= 0.4502

(b)(ii)
$\begin{array}{l}P\left(X>k\right)=\frac{480}{800}\\ P\left(Z>\frac{k-520}{40}\right)=0.6\\ \frac{k-520}{40}=-0.253\\ k-520=-10.12\\ k=509.88\end{array}$