In this paper an attempt has been made to calculate the producer's and the consumer's risks for non-normal populations. The effect of the peakedness parameter (kurtosis: λ4= β2– 3) only has been taken into consideration. In cases of platykurtic populations (λ4< 0), if the specification limits are set near the mean, then both the producer's and the consumer's risks will be greater than their respective normal theory values; and if the specification limits are set far from the mean, then both the risks will be smaller than their corresponding normal theory values. The situations will be the other way round in cases of leptokurtic populations (λ, > 0).