**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*ml*^{2}.
(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*) =

^{n}C_{r}. p^{r}. q^{n-r}
Probability, exactly 3 students are cycling to
school

*P*(

*X*= 3) =

^{9}C

_{3}(0.2)

^{3}(0.8)

^{6}

=
0.1761

**(a)(ii)**

At least a student is cycling to school

= 1 –

*P*(*X*= 0)
= 1 –

^{9}C_{0}(0.2)^{0}(0.8)^{9}
= 0.8658

**(b)(i)**

*m*

*=*520

*ml*

σ

^{2}= 1600*ml*^{2}
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)**

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