The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a standard deviation of 0.20 ounce. Every can that has more than 12.50 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)12.8760 ounces
B)12.0660 ounces
C)12.9340 ounces
D)12.1240 ounces

Question

Quizplus · Accepted Answer

To limit the spillage to 3%, the amount of soda that causes a spill (12.50 ounces) should correspond to the 97th percentile of the normal distribution (since 100% - 3% = 97%). Using the Z-score formula, Z = (X - μ) / σ, where X is the value from the distribution, μ is the mean, and σ is the standard deviation. The Z-score corresponding to the 97th percentile is approximately 1.88 (from Z-tables or statistical software). Rearranging the formula to solve for μ gives μ = X - Zσ. Substituting X = 12.50, Z = 1.88, and σ = 0.20 gives μ ≈ 12.50 - (1.88)(0.20) = 12.50 - 0.376 = 12.124 ounces.

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