The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a
Maximum of 12.75 ounces of soda. Every can that has more than 12.75 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).3413
B).6587
C).1587
D).8413

Question

Quizplus · Accepted Answer

To find the probability that a can will need to go through the special cleaning process, we need to calculate the probability that a can will have more than 12.75 ounces of soda. This is a problem involving the normal distribution, where we are given the mean (μ = 12.45 ounces) and the standard deviation (σ = 0.30 ounce). We need to find the Z-score for 12.75 ounces, which is calculated as $Z = \frac{X - \mu}{\sigma}$, where X is the value of interest (12.75 ounces). Plugging in the values, we get $Z = \frac{12.75 - 12.45}{0.30} = 1$. Looking up the Z-score of 1 in a standard normal distribution table or using a calculator, we find that the area to the left of Z=1 is 0.8413, which represents the probability of a can having 12.75 ounces or less. Therefore, the probability of a can needing the special cleaning process (having more than 12.75 ounces) is 1 - 0.8413 = 0.1587.

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