The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a standard deviation of 0.16 ounce. Every can that has more than 12.40 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that must be cleaned because of spillage to 3%?
A) 12.0992 ounces
B) 12.7008 ounces
C) 12.0528 ounces
D) 12.7472 ounces

Question

Quizplus · Accepted Answer

To limit the spillage to 3%, we need to find the mean such that the probability of dispensing more than 12.40 ounces is 3%. Using the z-score formula, we find the z-score corresponding to the 97th percentile (since 100% - 3% = 97%) is approximately 1.88. Using the formula: mean = 12.40 - (z-score * standard deviation), we get mean = 12.40 - (1.88 * 0.16) = 12.0992 ounces.

The Amount of Soda a Dispensing Machine Pours into a 12-Ounce