The existing algorithm employing the log-normal distribution lacks applicability in generating imprecise data. This paper addresses this limitation by first introducing the log-normal distribution as a means to handle imprecise data. Subsequently, we leverage the neutrosophic log-normal distribution to devise an algorithm specifically tailored for simulating imprecise data. During the generation of log-normal data, we systematically vary the degree of indeterminacy to observe its impact. Multiple tables will be presented to illustrate the influence of different degrees of indeterminacy across various mean and variance values. The application of a single sampling plan will be demonstrated using data generated by our proposed algorithm, contrasting it with results from the existing algorithm. Through simulation and practical application, our findings highlight the significant role played by the degree of indeterminacy in the data generation process from the log-normal distribution.