1 Test scores, \(X\), have mean 54 and variance 144. The scores are scaled using the formula \(Y = a + b X\), 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 \(b\).
\(235 \%\) of a random sample of \(n\) students walk to college. This result is used to construct an approximate \(98 \%\) confidence interval for the population proportion of students who walk to college. Given that the width of this confidence interval is 0.157 , correct to 3 significant figures, find \(n\).