Question

Individual bottles of water are filled by a machine at a factory with an amount of water that is approximately normal with a mean of 505 mL and a standard deviation of 1 Liter. A random sample of n =16 bottles is selected for a quality inspection. Calculate the standard deviation of the population (bottles) distribution in mL.

Answer 1

The standard deviation of the population (bottles) distribution for the amount of water filled by the machine is 1 liter or 1000 mL.

Step-by-step explanation:

The standard deviation of a population (σ) is the square root of the population variance (σ²). In this case, the standard deviation (σ) is given as 1 liter. To convert this to milliliters, we need to multiply by 1000 since 1 liter is equal to 1000 milliliters.

Mathematically, it can be expressed as σ = 1 liter × 1000 mL/liter = 1000 mL. Therefore, the standard deviation of the population distribution for the amount of water in the bottles is 1000 mL. This indicates the spread or variability of the water amounts in the population of bottles, with a standard deviation of 1000 mL around the mean of 505 mL.

When dealing with normal distributions, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. In this context, knowing the standard deviation is essential for understanding the variability and ensuring the quality of the water-filled bottles in the production process.