Infestations of Aphis gossypii per leaf in greenhouse cultivation of cucumbers were investigated to develop binomial sampling plans. An empirical $P_T-m$ model, $ln(m)={alpha}+{eta}ln[-ln(1-P_T)]$, was used to evaluate relationship between the proportion of infested leaves with ${leq}$ T aphids per leaf ($P_T$) and mean aphid density (m). Tally thresholds (T) were set to 1, 3, 5, 7, and 9 aphids per leaf to find appropriate T in greenhouse cultivation of cucumbers. Increasing sample size had little effect on the precision of the binomial sampling plan. However, the precision increased with tally threshold. The binomial model with T = 5 provided appropriate predictions of the mean densities of A. gossypii in the greenhouse cultivation of cucumbers. Using a binomial model with T = 5 (sample size = 200), a wide range of densities (1.2 - 222.8 aphids per leaf) could be estimated with precision levels of 0.346 - 0.380 for $P_T$ values between 0.15 and 0.96. Binomial models were validated at T = 5 and 7 using 12 independent data sets. Both binomial models were robust and adequately described aphid densities; most of the independent sampling data fell within 95% confidence intervals around the prediction model.