Final answer:
The lowest setting on the machine to minimize the number of chocolate drops less than 2 grams is option A: x - 0.02, which calculates the mass of the drops as close to 2 grams as possible without being under, based on the empirical rule.
Step-by-step explanation:
To minimize the number of chocolate drops less than 2 grams, we need to set the machine so that the lower end of the range of drop weights within two standard deviations of the mean is as close to 2 grams as possible without going under. Using the empirical rule, about 95% of the data falls within two standard deviations of the mean. Therefore, we need the lower end of this range (mean - 2 standard deviations) to be as close to 2 grams as possible.
If the setting of the machine is x, and we want the mass of the drops to be within two standard deviations, we calculate the lower boundary by subtracting two standard deviations from the mean (x - 2(standard deviation)). To ensure that this value is closest to 2 grams without being less than 2 grams, we'd choose the value of x such that this difference is maximized (highest setting) without going below 2 grams. The options provided are:
- A. x - 0.02
- B. x - 0.04
- C. x - 0.06
- D. x - 0.08
We do not have the value of the standard deviation in this case, but we can assume that the smallest option (A) would leave us closest to 2 grams without going under, thus minimizing the number of drops that are less than 2 grams. Therefore, the lowest setting of x to minimize the number of drops less than 2 grams is option A: x - 0.02.