The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.36 ounces and a standard deviation of 0.24 ounce. The cans only hold 12.60 ounces of soda. Every can that has more than 12.60 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process?
A) 0.1587
B) 0.8413
C) 0.6587
D) 0.3413

Question

Quizplus · Accepted Answer

To find the probability that a can will need to go through the special cleaning process, we calculate the probability that a can will have more than 12.60 ounces of soda. This is a right-tail probability in a normal distribution. We use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X = 12.60$, $\mu = 12.36$, and $\sigma = 0.24$. The Z-score is $Z = \frac{12.60 - 12.36}{0.24} = 1$. Looking up the Z-score of 1 in a standard normal distribution table or using a calculator, we find the area to the left is 0.8413. Since we want the area to the right (the probability of a spill), we subtract this from 1, giving $1 - 0.8413 = 0.1587$.

The Amount of Soda a Dispensing Machine Pours into a 12