A student titrates \(25.0 \text{ mL}\) of \(0.10 \text{ M NH}_3\text{(aq)}\) with \(0.10 \text{ M HCl(aq)}\) at \(25^\circ\text{C}\). The net ionic equation for the titration reaction is
\[ \text{NH}_3\text{(aq)} + \text{H}_3\text{O}^+\text{(aq)} \rightarrow \text{NH}_4^+\text{(aq)} + \text{H}_2\text{O(l)} \]
The student considers two acid-base indicators: methyl red (\(pK_a = 5.0\), color transition range \(\text{pH } 4.4\text{ to } 6.2\)) and phenolphthalein (\(pK_a = 9.4\), color transition range \(\text{pH } 8.2\text{ to } 10.0\)). Which of the following claims and justifications correctly identifies the more suitable indicator for detecting the equivalence point of this titration?