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A simple statistical model containing only one free parameter is proposed to account for the variability observed in a dosage–effect relationship between an integrated metric of noise exposure and the prevalence of annoyance in a community as synthesized by Schultz [J. Acoust. Soc. Am. 64, 377–405 (1978)]. The model assumes that a community’s noise dose is produced by long‐term noise exposure acting through a compressive transformation of the day–night average sound level (DNL). Individual reactions to this noise dose are characterized by a random variable. Individuals are assumed to report a consequential degree of annoyance when the value of this random variable exceeds a criterion level that is not a function of acoustic factors.