This article demonstrates that a normal fuzzy number can be constructed from earthquake waveform data. According to the RandomnessFuzziness Consistency Principle, two independent laws of randomness in [α, β] and [β, γ] are necessary and sufficient to define a normal fuzzy number [α, β, γ]. In this article, we have shown how to construct normal fuzzy numbers using data from earthquake waveform and have studied the pattern of the membership curve of the waveform.