Test scores, \(X\), have mean 54 and variance 144. The scores are scaled using the formula \(Y = a + bX\), where \(a\) and \(b\) are constants and \(b > 0\). The scaled scores, \(Y\), have mean 50 and variance 100. Find the values of \(a\) and \(b\). [4]

$50 = a + b \times 54$ | B1 | 

$100 = b^2 \times 144$ or $10 = b \times 12$ | B1 | 

$b = \frac{5}{6}$ or equivalent | M1 | Solving two simultaneous equations

$a = 5$ | A1 | [4] Both correct

Test scores, $X$, have mean 54 and variance 144. The scores are scaled using the formula $Y = a + bX$, where $a$ and $b$ are constants and $b > 0$. The scaled scores, $Y$, have mean 50 and variance 100. Find the values of $a$ and $b$. [4]

\hfill \mbox{\textit{CAIE S2 2011 Q1 [4]}}