The sampling distribution of a mean is a statistical method that might be employed for solving problems involving a considerably large number of samples. Statistical inference allows the researchers to calculate a statistic for each sample by repeatedly drawing samples from the selected population. Due to the variances in the results, it is possible to create a table demonstrating the values and their occurrence frequency. Because a sample statistic originates from the outcomes of multiple random samples of equal size, the method produces random variables. The variance might be computed by dividing the population variance by the sample size and suggests that an inverse relationship between the variables can be observed.

In business, the sampling distribution of a mean can be used to obtain data for evidence-based decision-making, market research, and product development based on analytical considerations. The sampling distribution might be helpful in the manufacturing business for testing product samples and improving quality control or reorganizing the production process. For example, the company producing eclectic vehicles decided to calculate the sampling distribution of a mean after the customers reported the problem of limited battery life.

To define the probability of customer dissatisfaction with the products, the z-table can be designed to display the percentage of the dissatisfied population. In the case of a normal distribution, the z-score formula can be calculated by dividing the difference between the test score and the mean by the standard deviation. The resulting score may suggest that the number of standard deviations is above or below the mean, or the population, measured during previous tests. Therefore, the data from the sampling distribution of a mean may be useful for making inferences about customer population and perceived product quality.