The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.54 ounces and a standard deviation of 0.36 ounce. Each can holds a maximum of 12.90 ounces of soda. Every can that has more than 12.90 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 probability that a randomly selected can will need to go through this process?
A) .1587
B) .3413
C) .8413
D) .6587

Question

Quizplus · Accepted Answer

The probability that a can will need to go through the cleaning process is the probability that the amount of soda exceeds 12.90 ounces. We calculate the z-score: z = (12.90 - 12.54) / 0.36 = 1. This corresponds to a probability of 0.1587 for z > 1 in a standard normal distribution.

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