Detection of hydroacoustic transmissions is a key enabling technology in applications such as depth measurements, detection of objects, and undersea mapping. To cope with the long channel delay spread and the low signal-to-noise ratio, hydroacoustic signals are constructed with a large time-bandwidth product, $N$. A promising detector for hydroacoustic signals is the normalized matched filter (NMF). For the NMF, the detection threshold depends only on $N$, thereby obviating the need to estimate the characteristics of the sea ambient noise which are time-varying and hard to estimate. While previous works analyzed the characteristics of the normalized matched filter (NMF), for hydroacoustic signals with large $N$ values the expressions available are computationally complicated to evaluate. Specifically for hydroacoustic signals of large $N$ values, this paper presents approximations for the probability distribution of the NMF. These approximations are found extremely accurate in numerical simulations. We also outline a computationally efficient method to calculate the receiver operating characteristic (ROC) which is required to determine the detection threshold. Results from an experiment conducted in the Mediterranean sea at depth of 900~m agree with the analysis.