Find the Value of a Normal Random Variable
-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 0.15 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)
A) 12.325 oz
B) 12.364 oz
C) 12.002 oz
D) 12.001 oz

Question

Quizplus · Accepted Answer

To ensure 98.5% of bottles contain at least 12 ounces, the mean should be set such that 12 ounces is at the 1.5th percentile of the distribution. Using the z-score for 1.5% in a standard normal distribution (approximately -2.17), and the formula for a normal distribution (mean + z * standard deviation), the mean is calculated as 12 + 2.17 * 0.15 = 12.325 ounces.