Question

QUESTION 1

Test marks for ten students are 2, 3, 6, 7, 7, x, 5, 5, 8, 9

(i) Given that the average mark is 6, find the value of x.

(ii) Calculate the standard deviation for these set of marks

QUESTION 2

Solve the following pair of equations by Cramer’s rule.

1) 3x + 5y = 2
2) 2x-7y = - 1

Answer 1

1.i)

$$x+2+3+6+7+7+5+5+8+9=6(10)$$

$$x+52=60$$

$$x=8$$

ii)

$$(2-6)^2+(3-6)^2+2(5-6)^2+(6-6)^2+2(7-6)^2+2(8-6)^2+(9-6)^2=46$$

The standard deviation for these set of marks:

$$s=\sqrt{\frac{46}{9-1}}=2.4$$

 2. The coefficient matrix is

$$\begin{bmatrix} 3 & 5 \\ 2 & -7 \end{bmatrix}$$

And

$$\begin{vmatrix} 3 & 5 \\ 2 & -7 \end{vmatrix}=3(-7)-2(5)=-31$$

So,

$$x=\frac{\begin{vmatrix} 2 & 5 \\ -1 & -7 \end{vmatrix}}{-31}=\frac{(2)(-7)-(-1)(5)}{-31}=\frac{9}{31}$$

$$y=\frac{\begin{vmatrix} 3 & 2 \\ 2 & -1 \end{vmatrix}}{-31}=\frac{(3)(-1)-(2)(2)}{-31}=\frac{7}{31}$$