Quality control is an important issue at a manufacturing company, which manufactures Product Z. To test the lifetime of Product Z, the company randomly sampled nine products and measured how many days they lasted (mean = 346.6). What is the standard deviation of the sample?

To determine the standard deviation of the sample, it is necessary to understand how it measures the dispersion or variability of the data points around the mean. The standard deviation provides insights into the consistency or reliability of the product's lifetime.

In this scenario, the company has a sample of nine products with an average lifetime. The correct standard deviation would indicate how much the individual lifetimes of Product Z vary from the mean of 346.6 days. Given the options provided, the selection of 58.5 suggests that there is a moderate degree of variability in the lifetimes of these products. This level of variability would be reasonable for manufactured products, which often experience differences due to variations in materials, processes, or other factors.

A standard deviation of 58.5 indicates that the lifetimes of the sampled products likely range significantly above and below the mean, an important aspect to consider in quality control. Monitoring the standard deviation helps the company identify whether the production process needs adjustments to ensure a more consistent product lifetime, which is crucial for customer satisfaction and operational efficiency.

Other options may suggest either too little variability or an excessive range from the mean, which might raise concerns about either the reliability of the product or the effectiveness of the manufacturing process. Thus, a