Inexact design has proved to be an efficient way of obtaining power savings with a marginal penalty on performance in applications which do not need high degree of output accuracy. Such applications are often found in domains which deal with human sensorial systems. The 'not so perfect' state of human senses like sight, hearing which are important for video and audio related appliances can compensate for the error introduced due to inexact design. An efficient analysis and modelling of these compensation capabilities of human senses can help the designers to build optimum inexact architectures meeting the redefined requirements with low power. In this work, we choose hearing aid as our test application, which is based on human sense of hearing. We estimate a metric Intelligibility, for a set of audio samples, which is obtained from multiple surveys on human subjects to model the sensorial processing. Our methodology uses a novel way of introducing inexactness in an optimum manner. This includes a fine grained analysis of the error that is being introduced in the FIR filters of the DSP present in hearing aid. The resulting inexact FIR filter bank is 1.92× or 2.56× more efficient in terms of power consumed while producing 10% or 20% less intelligible speech respectively when compared with a hearing-aid using exact filters.