Optimistic Analysis on Soft Drink Machine Data

How can the manufacturers claim the accuracy of their soft drink machines?

The manufacturers want to advertise that 90% of cups will contain 200±d mL of soft drink. What is d?

Answer:

The 'd' value that allows the soft drink machine manufacturers to claim that 90% of cups will contain 200±d mL is approximately 16.45 mL.

To showcase the accuracy of their soft drink machines, the manufacturers have set a goal of ensuring that 90% of the cups dispensed will contain a volume of soft drink within the range of 200±d mL. This indicates that they aim to maintain consistency in the quantity of beverage dispensed to the customers.

In statistical terms, the value of 'd' represents the margin of error or deviation around the average quantity of 200 mL. By calculating the appropriate 'd' value, the manufacturers can confidently assert that the vast majority of cups will meet the specified volume range.

To derive the value of 'd' in this scenario, we utilize the concept of normal distribution and Z-scores. By considering the mean volume of 200 mL and the standard deviation of 10 mL, along with the desired coverage of 90% of data points, we arrive at the calculated value of approximately 16.45 mL for 'd'.

By adopting such a precise approach towards their soft drink machines, the manufacturers not only enhance customer satisfaction by ensuring consistent serving sizes but also bolster their brand reputation for reliability and accuracy in beverage dispensing.