The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution witha mean of 12.48 ounces and a standard deviation of 0.32 ounce. The cans only hold 12.80 ounces of soda. Everycan that has more than 12.80 ounces of soda poured into it causes a spill and the can needs to go through aspecial cleaning process before it can be sold. What is the probability a randomly selected can will need to gothrough this process?
A) 0.1587
B) 0.3413
C) 0.8413
D) 0.6587

Question

Quizplus · Accepted Answer

To find the probability that a can will overflow and require cleaning, we calculate the Z-score for 12.80 ounces using the formula Z = (X - μ) / σ, where X is 12.80 ounces, μ is 12.48 ounces, and σ is 0.32 ounces. This gives us Z = (12.80 - 12.48) / 0.32 = 1. The probability of a Z-score being less than 1 is 0.8413, so the probability of a can needing cleaning (Z > 1) is 1 - 0.8413 = 0.1587.

The Amount of Soda a Dispensing Machine Pours into a 12