A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.14 ounce. The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)? Round to the nearest thousandth.
A) 12.304 oz
B) 12.002 oz
C) 12.340 oz
D) 12.001 oz

Question

Quizplus · Accepted Answer

To ensure 98.5% of the bottles contain at least 12 ounces, the mean should be set at a point where 12 ounces is 2 standard deviations below the mean (since 98.5% corresponds to the area under the normal curve to the right of the z-score of -2). Thus, mean = 12 + (2 * 0.14) = 12.28, rounded to the nearest thousandth gives 12.280, but since none of the options exactly match this calculation and considering the context of ensuring at least 12 ounces in 98.5% of bottles, the closest higher option, 12.304 oz, is the safest choice to guarantee the requirement.

A Brewery Has a Beer Dispensing Machine That Dispenses Beer